given athlete has 60% chance of joining. find min. number of

[Bravo75]

I need somewhere to start...any clue would be greatly appreciated:

Question: A Coach is recruiting for his team. From past knowledge, he knows that an athlete whom he talks to has a 60% chance of joining his team.

-What is the minimum number of athletes he should contact so that the probability of at least 6 recruits is 80% or higher?

-If he contacts 9 players, what is the expected number of the 9 who will join the team?
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I'm new to these boards, and am not entirely sure how help here works, but I'm just looking for a way to get started on this problem...I don't know why I'm drawing such a blank.

Thanks for the help!

 

[chivox]

Re: Recruiting for a team with probability 60%

I'm not sure about the answer, but think of what probability means. All you really have to find here is the boundary value, since you want the "minimum" number. Probability is generally represented by the number of desired outcomes over the number of total outcomes. That value has to be greater than or equal to .8 for some number of people the coach talks to. So, how many outcomes are we talking about in this problem?

We want six people to be recruited out of some number that we talk to. That sounds like "some number, choose 6" which we can represent:

n! / (6! * (n-6)!)

I think that would represent the total number of desirable outcomes, where six would be recruited. You would have to add to the number of desirable outcomes the number for nC7, nC8, ... nCn, because these would also satisfy the conditions of the problem. It is important to note that the probability for each student, independent of the other students being recruited is 60%. The variable n, which you would have to find, would represent the number of people the coach would have to talk to, from which he would choose 6 or more.

But what number should go in the denominator? Well, we're going to talk to n people, recruiting 6...n of them. The total number of outcomes would be that number PLUS the number of outcomes where we choose 0, 1, 2, 3, 4, or 5 people. Then you have to set that probability greater than or equal to .8 somehow and solve for n.

Good question. Keep thinking.

 

[Bravo75]

Re: Completely Stumped

Thanks Chivox,

I'll try to take this and run with it. It's a rather complex problem for me...but hopefully I'll be able to work through it.