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 group of 10 will ininclude 5 women and 5 men (round to 4 decimal places)? B) List all possible makeups of the group that have a probability of less than 1% (round to 4 decimal places). C) Is the probability distribution symmetric or skewed and why?

Solution

A)

There are 96C10 = 1.12799*10^13 ways to choose 10 people.

Now, there are 54C5 = 3162510 ways to choose 5 boys, and 42C5 = 850668 ways to choose 5 girls.

Hence there are 3162510*850668 = 2.69025E+12 ways to choose 5 boys and 5 girls.

Thus,

P(5 boys and 5 girls) = 2.69025*10^12 / 1.12799*10^13 = 0.238498546 [ANSWER]

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B)

0.00013

In this case, we see that those with probability less than 1% are (0 boys, 10 girls), (9 boys, 1 girl), (10 boys, 0 girls). [ANSWER]

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c)

It has to be skewed, as there are unequal number of boys and girls, so it cannot be symmetric.