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.
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.
To calculate P(man is a ballet dancer and a musical performer), you will need to use the conditional probability formula:
P(man is a ballet dancer and a musical performer) = P(man is a ballet dancer) * P(man is a musical performer | man is a ballet dancer)
Given the information provided, we know that the probability a man is a ballet dancer is 0.245 and the probability a man is a musical performer, given that he is a ballet dancer, is 0.250.
So, substituting these values into the formula:
P(man is a ballet dancer and a musical performer) = 0.245 * 0.250
P(man is a ballet dancer and a musical performer) = 0.06125
Therefore, the probability that a man is a ballet dancer and a musical performer is 0.06125, or approximately 6.125%.
To calculate P(man is a ballet dancer and a musical performer), you need to use the information given and apply conditional probability.
Let's start by using the given probabilities:
- P(man is a ballet dancer) = 0.245
- P(man is a musical performer | ballet dancer) = 0.250
Now, we need to find P(man is a musical performer). We are not directly given this probability, but we can still calculate it by using the probabilities of the events mentioned in the irrelevant information.
From the irrelevant information:
- P(woman is a musical performer) = 0.365
- P(woman is an actress) = 0.550
- P(woman is an actress | musical performer) = 0.785
Since we are only interested in the probabilities for men, we can ignore the information about women.
We know that the probability of an event A given event B can be calculated using the formula:
P(A | B) = P(A and B) / P(B)
In this case, the event A is "man is a musical performer" and the event B is "man is a ballet dancer."
We want to find P(man is a musical performer) = P(A).
To find P(man is a musical performer) = P(A), we can use the probability of a woman being a musical performer as a reference. Since the question provides no explicit information about the probability of a man being a musical performer, we can assume it is the same as that of a woman.
Therefore, we can estimate P(man is a musical performer) ≈ P(woman is a musical performer) = 0.365.
Now, to calculate P(man is a ballet dancer and a musical performer), we can use the formula for conditional probability:
P(man is a ballet dancer and a musical performer) = P(man is a musical performer | ballet dancer) * P(man is a musical performer)
Substituting the given values:
P(man is a ballet dancer and a musical performer) = 0.250 * 0.365
Calculating the result:
P(man is a ballet dancer and a musical performer) ≈ 0.09125
Therefore, the estimated probability that a man is both a ballet dancer and a musical performer is approximately 0.09125.