A population consists of 25 men and 25 women. A simple random sample (draws at random without replacement) of 4 people is chosen. Find the chance that in the sample:
a)the fourth person is a woman
b)the third person is a woman, given that the first person and fourth person are both men
[Math] the chance that the fourth person is a woman
probability
Best Answer
Imagine drawing people, one after the other, until we have drawn all $50$. Then all orderings of the people are equally likely.
So the probability the fourth person is a woman is the same as the probability that the first person is a woman, which is $\frac{25}{50}$.
Similarly, the probability that the third person is a woman, given that the second and fourth are men, is the same as the probability the third is a woman, given the first two are men. This is $\frac{25}{48}$.