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A school student body has 40% male and 60% female. Six of the students will randomly be chosen for a scholarship.

a) what is the probability of 3 or more males being chosen?

b) what is the expected number of males who are winners?

c) assume students are chosen one at a time - what is the probability that the 4th student chosen will be the 3rd male student chosen?

Pretty stumped with this one... thanks for the help

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    $\begingroup$ Please share what you've tried before asking for help. As a hint, this problem is related to the binomial distribution. $\endgroup$ – Green Oct 13 '17 at 0:14
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    $\begingroup$ It should be pointed out that without information about how large the student body actually is, our only way to approach would be to assume that it is "very large" and that sampling with replacement will provide us with a reasonable approximation. Of course, if there are only ten students in the entire student body population as a whole, then the approach will be very different. $\endgroup$ – JMoravitz Oct 13 '17 at 0:44
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    $\begingroup$ That being said, this problem should remind you very closely of similar problems such as "what is the probability of flipping 3 or more heads out of six flips with an unfair coin" $\endgroup$ – JMoravitz Oct 13 '17 at 0:47
  • $\begingroup$ sorry, yes i was confused because the population number was not specified.. $\endgroup$ – jc315 Oct 13 '17 at 0:59
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    $\begingroup$ Correct, we do not in fact need to know. I will stress however that using the binomial distribution approach is an approximation and the exact answer will depend on the exact population size. It is however a going to be a very good approximation, likely off by less than a billionth of a percent. $\endgroup$ – JMoravitz Oct 13 '17 at 1:17

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