Question

Professor Stats has 40 students in her statistics class. 24 of the students are male. If she randomly selects 6 of her students at random, without replacement, the probability of selecting 4 men in the sample is

Answer 1

Answer: 0.332...

Explanation:

We know it's a hypergeometric distribution from the term "without replacement," so we can use the hypergeometric formula:

P(X=x)= ([s]C[x] * [N-s]C[n-x]) / [N]C[n]

What we are given:

- N (number of items in population = 40

- n (sample size) = 24

- s (population successes) = 6

- x (sample successes) = 4

Which means:

- N-s = 40-6 = 34

- n-x = 24-4 = 20

Now to plug it into the formula:

([6]C[4] * [34]C[20]) / [40]C[24]

To break that down

- [6]C[4} = 6! / (4! * (6-4)!) = 15

- [34]C[20] = 34! / (20! * (34-20)!) = 1,391,975,640

- [40]C[24] = 40! / (24! * (40-24)!) = 6.285210165 * 10^10

SO TO PLUG IN

(15 * 1,391,975,640) / 6.285210165 * 10^10

= 0.332202647992... or just 0.332

Answer 2

the answer is 332

Explanation:

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