I'm doing some research on public knowledge of probability. If anybody could spare the time to answer the following questions I'd be very grateful. I need as many people as possible to answer and it would be good if you post your answers before reading other peoples. Don't worry that others will see your wrong answers there were degree level mathematicians that made mistakes on these.


1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?


2.Why do you need to roll a 6 to start in many games?



3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45

4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?



6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?



7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?



8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?



9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?



10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?



11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?

1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?
50/50 chance to get heads or tails.

2.Why do you need to roll a 6 to start in many games?
(assuming we're talking about rolling a D6 for a board game)
6 is the highest number on a 6 sided dice and those rolling the highest means going first.

3.Which of these two sets of numbers is most likely to win the lottery?
Neither, both have the same chance of getting drawn at random. (although I know I would pic B if given the choice)

4.If I roll a pair of dice which of the following am I more likely to get?
(A) 7 is the average number when 2 dice are rolled.

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?
You're more likely to get heads 2 out of 3 times because the more attempts one takes the closer the 50/50 probability is.

6.In the first round of a gameshow 3 numbers are drawn randomly from 12 and in the second round 9 are drawn randomly from 12? Are you more likely to match the numbers in the first round or the second round?
I would assume second round.

7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?
Black

8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?
White

9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?

9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?
50% (?)

10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?
Same chance to be a boy or a girl.

11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?
Yes (assuming the dice isn't rigged)

Here goes nothing

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Originally Posted by v1033

1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?Neither as they are both equally possible.


2.Why do you need to roll a 6 to start in many games? The highest number on a standard die.



3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45
Neither, both sets have the same chances, in the UK that is around 14 Million to 1

4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s
Both the same. 1in6 and 1in6 for any number on a 6 sided die.

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?

I'd say the larger sample.



6.In the first round of a gameshow 3 numbers are drawn randomly from 12 and in the second round 9 are drawn randomly from 12? Are you more likely to match the numbers in the first round or the second round?
Not sure about this as you haven't mentioned what numbers are meant to be matched.



7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?
Black 2/3 chance, assuming you replaced the first marble otherwise 1/2



8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?
Either as they are both equally possible for the first draw.


9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?

It's always 25%, doesn't matter how many children they have.



10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?
Either are likely, again 1/2



11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?
Yes as they both have the same chance of throwing the required number, assuming they need that excat number to win.

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Thanks for the replies so far. I don't think I explained question 6 very well.

6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?

Still doesn't really make sense.
What numbers are being matched ?

Scrub that, would help if I could read.
Hey it is late ;)

Second round

1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?

I would have a 50/50 chance of getting either heads or tails. It is a 2 sided coin.


2.Why do you need to roll a 6 to start in many games?

That would be the rules of the games, maybe because it is the highest number on a dice.



3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45

B--would be more likely to win the lottery


4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s

a three and a four

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?

2 heads out of three.

6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?

second round because there was more numbers to choice from.

7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?

It is a 50/50 chance it will be either white or black. Because you have both left in the bag.

8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?

It will be either white or black. It is a 50/50 chance. Also color is spelled COLOR--not colour.

9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?

25% chance for each child.

10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?

It is a 50/50 chance. Actually it is up to the y chromosome--so it is up to the man. But in all actuality it is a 50/50 chance.

11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?

yes.

Anyone else fancy a go? I will post the correct answers on Saturday if anyone is interested. Just FYI no-one has them all right yet...

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Originally Posted by v1033

I'm doing some research on public knowledge of probability. If anybody could spare the time to answer the following questions I'd be very grateful. I need as many people as possible to answer and it would be good if you post your answers before reading other peoples. Don't worry that others will see your wrong answers there were degree level mathematicians that made mistakes on these.


1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails? Your odds will still be 50/50


2.Why do you need to roll a 6 to start in many games? ?


3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45
they are equally as likely

4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s
they are equally as likely

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?
2 out of 3



6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?
He is more likely to match all numbers in the first round. More likely to match one number in the second round


7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?
Black


8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?
Black



9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?
50%


10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?
Equal odds


11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair? Yes

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Good luck with the study

Correct Answers...

1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?
neither are more likely

2.Why do you need to roll a 6 to start in many games?
Just convention - it is no less likely than any other number


3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45 they are equally likely

4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s a 3 and a 4

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?2 out of 3

6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?
equal chance in either round

7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?

black

8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?

black

9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?
43.75%

10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?

equal chance of either

11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?
yes

I dont have time to write all the explanations now (as I late for my aerobics class) but if anyone has any questions i'll be on amhd later and will answer them then...

Thanks for your help :-0

If you were really doing research, you wouldn't (or shouldn't, anyway) be asking on a Math forum, or any forum for that matter. You are giving people the ability to answer or not, as people who know the answers are more likely to respond than those who do not, thus skewing your results.

Quite ironic when you think about it.

But after reviewing your questions, they seem to be copied from memory or thrown out at random, since a few of them cannot be answered based on the information given.

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Originally Posted by EuRa

If you were really doing research ? are you suggesting that my life is so dull i sit at home pretending to research people's mathematical misconceptions on the internet?, you wouldn't (or shouldn't, anyway) be asking on a Math forum, or any forum for that matter. You are giving people the ability to answer or not, as people who know the answers are more likely to respond than those who do not, thus skewing your results.yes i know that, it's kind of the point

Quite ironic when you think about it.not really but it is interesting that you know more about my aims than me

But after reviewing your questions, they seem to be copied from memory no i'm afraid i wrote them myself and that's why i had to edit number 6 as it made no sense to anybody except me or thrown out at random all of the questions have a specific purpose but to have stated the purpose would have skewed the results, since a few of them cannot be answered based on the information giventhat's weird all of my year 11s answered them without extra information.

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anyway better be off have some fake research to do on local ales x

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Originally Posted by v1033

If you were really doing research ? are you suggesting that my life is so dull i sit at home pretending to research people's mathematical misconceptions on the internet?, you wouldn't (or shouldn't, anyway) be asking on a Math forum, or any forum for that matter. You are giving people the ability to answer or not, as people who know the answers are more likely to respond than those who do not, thus skewing your results.yes i know that, it's kind of the point

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I wasn't suggesting this, honestly. I was merely saying that if you really are trying to get accurate research, posting on the forum isn't a good idea, especially for a college paper. I had the initial feeling that you found these questions somewhere and found them fun, so you wanted to post them here, which is cool, but after reading them I began to think otherwise.

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Quite ironic when you think about it.not really but it is interesting that you know more about my aims than me

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You don't think that it's ironic? Giving probability questions on a forum, claiming it's for research, yet the answers given will be mostly inaccurate because you are choosing your participants instead of doing it at random! I do, heh.

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But after reviewing your questions, they seem to be copied from memory no i'm afraid i wrote them myself and that's why i had to edit number 6 as it made no sense to anybody except me or thrown out at random all of the questions have a specific purpose but to have stated the purpose would have skewed the results, since a few of them cannot be answered based on the information given that's weird all of my year 11s answered them without extra information.

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Anyone can answer the questions, even if they aren't properly given or written. If I say I have a bag of socks, 50 of them are red, how many are blue, and I get 11 answers, that doesn't mean it's a legit question.

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Originally Posted by v1033

2.Why do you need to roll a 6 to start in many games?
Just convention - it is no less likely than any other number

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As soon as I got to this question, I stopped. NEED A 6? I've never ever played a game where I NEEDED a six. Ever. This isn't even a probability question. If you NEEDED a 6, it would have to be in the rules of the game or something. I assumed that if several people were playing, someone would need to roll a six to get the highest roll to determine who goes first. Your answer is even more confusing to me.


Number 6 didn't make sense at all when you originally wrote it. It's worded well now... and I like it a lot. I'll probably steal it and use it myself.

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9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?
43.75%

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This is also worded oddly. "Jenny AND Aadi" is different than "Jenny OR Aadi", which is what I think you meant. AND gives you a different answer than OR.

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10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?
equal chance of either

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Male sperm are faster than female sperm, so technically a boy is more likely. You have to assume that the sperm are equally as fast, or say something of the sort at the start. (ie - assuming the probability of having a boy or a girl for all couples is 50-50... )

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11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?
yes

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If you are using 1 die, sure. Not with 2, which I originally assumed because more games I play use 2. Since this information isn't given, I have no idea if it's fair or not.


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All these reasons are why I didn't answer any of the questions. Sure, other people answered them, but there is still information missing.

I know I'm totally being "that guy", but I think it's important to note that questions such as these have to be worded clearly and precisely, especially if you are looking for the results you claim you want. I have a feeling many of the answers given are going to be wrong for the wrong reasons, and you need to take that into consideration. According to your answers, I would have had a few wrong, but that wouldn't have been my fault.

Based on your posts in this forum, you seem verbose and intelligent. Most of these problems even have grammatical errors. It's more likely that you found this questionnaire somewhere, and copy and pasted it with very little editing (if any). I don't like it, it's written poorly, and could have some promise with a little editing.

1.If I toss a fair coin 3 times and get 3 heads in a row, on the next toss will I be most likely to get heads or tails?

--Both will be equally likely. (50% probability)

2.Why do you need to roll a 6 to start in many games?

--Interesting... I think it's just because hmmm, people have the tendency to think that we are less likely to obtain a 6, and so is 'difficult' to start. Anyway, if any other number was to be chosen instead, the probability would be same.

3.Which of these two sets of numbers is most likely to win the lottery?

a) 1 2 3 4 5 6 b) 4 16 20 29 34 45

--I would definitely say a), given that all each of the 6 numbers may range from 0-9 and the numbers in b) from 0-99

4.If I roll a pair of dice which of the following am I more likely to get?

a) a 3 and a 4 b) two 4s

--Both equally likely.

5.When tossing a fair coin are you more likely to get at least 2 heads when you toss it 3 times or to get at least 200 heads when you toss it 300 times?

--I think it is the first one, 2 out of 3, because the more you toss, the more it is supposed to tend to the ratio 1:2

6. In a gameshow there are 12 balls marked 1 through 12.
In the first round the contestant picks 3 numbers and then 3 balls are drawn randomly from the 12.
In the second round the contestant picks 9 numbers, the balls from round one are replaced and then 9 balls are drawn randomly from the 12.
Is the contestant more likely to match the numbers in the first round or the second round?

--I would say the second round.

7.I have 2 black marbles and 2 white marbles in a bag. I take out marbles without looking. The first marble I pick out is white. I pick out a second marble, what colour is it most likely to be?

--Black, if you're not replacing the white marble.

8.I have 2 black marbles and 2 white marbles in a bag. I pick out a marble and put it aside without looking at it. I then pick out a second marble and see that it is white. What colour is the first marble most likely to be?

--Black

9.The probability of Jenny and Aadi passing on a genetic condition to their child is 25%. If they have 2 children what is the probability that at least one of the children will have the condition?

-- 5/16

10.Another couple have 4 boys. Is their next child more likely to be a boy or a girl?

-- Both are equally likely.

11.At the end of a game Simon needs to roll a 6 to win and Caoimhe needs to roll a 3. Is this fair?

--Yes, both numbers have a 1/6 probability to win.

Woops, just found out that you already posted the answers... :o

Lol, you said that the better was not to look at the others' responses... which was what I did and missed the post where you gave off the answers... :o

Two reactions:

1. First, a suggestion for improvement - like a few others, when you talked about rolling a 6 (or whatever) I assumed you meant using two dice, not one. You should explicitly state that you are using 1 die.

2. I like question 6 - it was the only one for which my initial "gut" reaction was wrong. It's the kind of question you can pose to colleagues at the lunch table and get quite a lively discussion going. However, to make it clearer, you should explicitly state that in each round the balls are drawn without replacement. Other than that - nice question!