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The class of 2015 at a college, with a graduation rate of 60%, has 250 students. What is the probability that:

1) all the student will graduate in four years?

2) half of the students will graduate in four years?

3) exactly 75% of the students will graduate in four years?

user3254506
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  • Can you post what you've tried so far? (1) is pretty straightforward. – GMB May 15 '14 at 23:30
  • I'm new to this but if it is as easy I thought it is, then for one student (1/250) to graduate its: (1/250)60%, right? Then for all students, then (250/250)60%; for half (125/250)60%; and for the last is: (x/250)60% = 75% where i solve for x ? – user3254506 May 15 '14 at 23:47
  • Not quite, no - I'll post an answer. Thanks for sharing your thoughts. – GMB May 15 '14 at 23:59

1 Answers1

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The odds of any one student graduating is $0.6$. When you need to "and" together the probabilities of two (independent) events - for example, Alice graduates AND Bob graduates - you multiply. So the probability that two given students both graduate is equal to $0.6^2$, and the probability that $250$ given students all graduate is $0.6^{250}$. That's (1).

Here's a question: what is the probability that $k$ students graduate, and the remaining $250-k$ students don't? For each possible set of $k$ students, we're going to need to find the probability that they graduate and their peers don't, and then add this probability up over all possible sets. The probability for any one set is $0.6^k 0.4^{1-k}$ (do you see why? It's the same multiplication trick as before). The number of sets is just $250 \, C \, k$ - are you familiar with "choose" combinatorics? Anyways, maybe that will be enough of a hint to get (2).

I'm a little confused by (3). Exactly $75\%$ of $250$ is $187.5$, and you're not going to have half a student graduating. Maybe the answer is $0$? Maybe they mean exactly $188$ students graduating? Your call.

GMB
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