Statistics  Probability
posted by Michael .
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 2235 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 2235…
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.

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.