# Probability quiz for fun

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?

 RedJoe Posts: 3, Reputation: 5 New Member #2 Dec 31, 2008, 11:13 AM
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)
 Curlyben Posts: 18,070, Reputation: 8728 Admin & Wine Expert #3 Dec 31, 2008, 11:22 AM
Here goes nothing
Quote:
 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.
 v1033 Posts: 44, Reputation: 18 Junior Member #4 Dec 31, 2008, 02:59 PM
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?
 Curlyben Posts: 18,070, Reputation: 8728 Admin & Wine Expert #5 Dec 31, 2008, 03:06 PM
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
 pa46226 Posts: 12, Reputation: 8 New Member #6 Dec 31, 2008, 03:32 PM
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 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?

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 why 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.
 v1033 Posts: 44, Reputation: 18 Junior Member #7 Jan 1, 2009, 02:55 PM
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...
 jjwoodhull Posts: 1,378, Reputation: 1210 Ultra Member #8 Jan 1, 2009, 03:06 PM
Quote:
Good luck with the study
 v1033 Posts: 44, Reputation: 18 Junior Member #9 Jan 3, 2009, 01:26 AM

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 don't 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...

 EuRa Posts: 315, Reputation: 335 Full Member #10 Jan 4, 2009, 08:23 AM
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.
v1033 (Jan 4, 2009 09:32 AM): post is unhelpful, irrelevant and unconstructive...   Source:

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