Question

I need to calculate P(man is a ballet dancer and a musical performer) given the following information...

In a random sample of male and female graduates of the New York School for the Arts between the ages of 22-35 you know that:
the probability a man is a ballet dancer is 0.245.
the probability a man is a musical performer, given that he’s a ballet dancer is 0.250.

(Also, I don't believe this information is relevant: the probability a woman is a musical performer is 0.365; the probability a woman is an actress is 0.550; the probability a woman is an actress, given that she’s a musical performer is .785.)

Here's the work I've done so far:
This cannot actually be computed. However, we can compute the conditional probability given than the man is between the ages of 22-35…
P(man musical performer | ballet dancer) does not equal P(musical performer), so the events are dependent. P(man musical performer | ballet dancer) = P(man musical performer and ballet dancer) / P(man musical performer).
Therefore, P(man musical performer and ballet dancer) = P(man mp | bd) * P(mp)

However, the probability a man is a musical performer is unknown, so I am unsure how to compute that.

Answer 1

I am confused too. If "the probability a woman is an actress is 0.550", how can the probability a woman is an actress, given that she’s a musical performer be .785. Do you mean .785 of the .550?

The same applies for the man as a ballet dancer.

I hope this helps. Thanks for asking.