Question

In: Statistics and Probability

Among the contestants in a competition are 49 women and 29 men. If 5 winners are...

Among the contestants in a competition are 49 women and 29 men. If 5 winners are selected, what is the probability that they are all women?

Solutions

Expert Solution

There are 2 ways to solve this problem.

the contestants in a competition are 49 women and 29 men. So that makes a total of 78 contestants.

Method 1:

P(First woman is selected )=

For the second woman to be selected we have 48 choices out of 77 contestants. For the 3rd woman to be selected we now just have 47 woman left to choose out of 76 contestants and so on till 5th woman is selected in 45 ways out of 74 contestants

Hence, the probability that they are all woman

The probability that they are all woman = 0.09032617

Method 2:

5 women are selected out of 49 women in ways and hence the probability of selecting all 5 female candidates is given by

orchestra answered 2 years ago
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