Question

question 24 of 25
in a concert band, the probability that a member is in the brass section is
0.50. the probability that a member plays trumpet, given that he or she is in
the brass section, is 0.36.
what is the probability that a randomly selected band member is in the brass
section and plays trumpet?
a. 0.18
b. 0.72
c. 0.86
d. 0.14

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), where \(P(A|B)\) is the probability of event \(A\) given event \(B\), \(P(A\cap B)\) is the probability of both \(A\) and \(B\) occurring, and \(P(B)\) is the probability of event \(B\) occurring.

Step2: Identify the values from the problem

Let \(A\) be the event that a member plays trumpet and \(B\) be the event that a member is in the brass section. We are given \(P(A|B) = 0.36\) and \(P(B)=0.50\).

Step3: Solve for \(P(A\cap B)\)

Using the formula \(P(A\cap B)=P(A|B)\times P(B)\), substitute the values: \(P(A\cap B)=0.36\times0.50 = 0.18\)

Answer:

A. 0.18