1. ## Probability question

A teacher says 40% of students study for a specific test. If she randomly selects 5 students, whats the probability that 3 studends did not study for the test?

So i tried to solve it like this but im not sure if its the right way. I assumed that since the problem is giving you a percentage we can say that out of 100 40 studied and 60 did not:
(60C3)(40C2)/(100C5)
Is this thw correct way to do it?

2. ## Re: Probability question

This sounds to me like a binomial probability distribution problem. Your calculation is a hypergeometric equation. But you don't really know the finite quantity of the population. So, you could consider 40% as the success rate and 60% as the failure rate in a binomial problem. The probability that 3 students did not study means that 2 students did study out of the 5 students sampled.

So, using the binomial formula: (5 C 2)*(0.4)^2 *(0.6)^3 = 0.346

The probability is an approximation that is pretty good as long as the sample size is no more than 5% of the total population. Anyway, that's what I'm thinking. Hope this helps!

3. ## Re: Probability question

Originally Posted by spengel
This sounds to me like a binomial probability distribution problem. Your calculation is a hypergeometric equation. But you don't really know the finite quantity of the population. So, you could consider 40% as the success rate and 60% as the failure rate in a binomial problem. The probability that 3 students did not study means that 2 students did study out of the 5 students sampled.

So, using the binomial formula: (5 C 2)*(0.4)^2 *(0.6)^3 = 0.346

The probability is an approximation that is pretty good as long as the sample size is no more than 5% of the total population. Anyway, that's what I'm thinking. Hope this helps!
Oh crap, yea you are correct. I totally forgot using the binomial formula in the exam! Well as an answer i got around 0.35 hopefully the professor does not mark it wrong. Thanks.

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