A large college class has 54 women and 42 men as students Te

A large college class has 54 women and 42 men as students. Ten of the students are chosen at random.

A) what is the probability that the chosen of 10 will include 5 women and 5 men? Give your answer to 4 decimal places.

B) list all possible makeups of the group that have a probability of less than 1%. Give your probability to 4 decimal places.

C) is the probability distribution symmetric or skewed? justify your answer

Solution

a) to select 5 women out of 54 , number of ways =54C₅

to select 5 men out of 42 , number of ways =42C₅

total ways =54C₅*42C₅

sample space n(s)=106C₁₀

probability=54C₅*42C₅/106C₁₀