6. Parts produced by a certain company have a probability of 1/20 of being defective. A group of 10 of these parts are inspected.

(a) Find the probability that four of the parts are defective
(b) Find the probability that at least one of the parts is defective.
c) Find the probability that all the parts are defective.
(d) find the probability at most one of the parts are defective.

(e).Find the mean(expected) number of defective parts for the sample and the standard deviation.

7. 2000 raffle tickets are sold for $4 apiece. There is one $500 prize, two $250 prizes and four $100 prizes.
(a) Find the expected value of a person buying one ticket.

(b) If a person buys 10 tickets what is the probability that they win at least one of the prizes? (to answer this question approximate this as a binomial distribution where p is the probability of getting a winning ticket)

4. Find the following probabilities:
(a) randomly answering the first three questions correctly and the last two incorrectly on a five question multiple-choice quiz. (There are four possible answers to each question)


(b) drawing three cards from a deck without replacement and getting at least one heart.

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I did answer it not right it practice for a reason.. I have no answers it not homework.. it just different question. Not grade is give for this.. I just want to learn how to do this.. please help.. it would help do others I have.

For a I think is 1/52
For 4 b I got 13/52*12/51*11/50
For

I did answer it not right it practice for a reason .. I have no answers it not homework .. it just different question. not grade is give for this .. I just want to learn how to do this .. please help.. it would help do others I have.

4 a i think is 1/52
for 4 b i got 13/52*12/51*11/50
for
I'll help you with question 4. Hopefully that will show you the technique to help with the other problems as well. If not, tell us where you get stuck and we'll guide you further.

4 (a) To compute the probability of ALL of those things happening (i.e. answering the first, second, and third questions correctly and the fourth and fifth incorrectly), you need to simply multiply the probabilities of each of those events occurring independently.

So what's the probability of randomly getting the right answer with four possible choices? Well, there's one right answer out of four choices, which means your probability is one out of four (i.e. 1/4 or 0.25).

Meanwhile, how about the probability of getting a wrong answer? There are three wrong answers out of four choices, so what does the probability work out to?

Your final answer will be
P(overall) = P(1 is right) x P(2 is right) x P(3 is right) x P(4 is wrong) x P(5 is wrong)

What does that work out to be?

4(b) In this case, since it's asking about the probability of "at least one", it's much easier to compute the chances that you DON'T get a heart. Then, to find the chances that you DO get at least one, you simply subtract your answer from 1.

For the very first draw, there are 52 cards in the deck, 39 of which are NOT hearts. So your probability of drawing a non-heart is 39/52. For the second draw, there are now only 51 cards remaining and only 38 of them are non-hearts, so your probability on this draw is 38/51. You can use the same logic to find the probability for the third drawing.

Now, just multiply the probabilities of all three events to get the overall probability that you draw NO hearts. Your answer should be something a little over 40% (I'll leave it to you to find a more precise answer than that). That means that the probability that you DO draw at least one heart is 1 minus that number, or a little under 60%.