Question

Suppose that a high school marching band has 125 members. Of these 125 band members, 41 are seniors, 24 play the trumpet, and 10 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet

Answer 1

Answer:

The probability is 42%

Step-by-step explanation:

Conditional Probability

It's the probability of the occurrence of an event B knowing that an event A has already occurred and A and B are related (not independent).

If P(A) is the probability of occurrence of A, $P(A\cap B)$ is the probability of both events to occur, and P(B|A) is the required probability occurrence of B:

$\displaystyle P(B|A)=\frac{P(A\cap B)}{P(A)}$

We know a high school marching band has 125 members, from which 41 are seniors (event B), 24 play the trumpet (event A), and 10 are seniors who play the trumpet.

The probability that a randomly selected band member plays the trumpet is

$\displaystyle P(A)=\frac{24}{125}$

The probability that he or she has both attributes is

$\displaystyle P(A\cap B)=\frac{10}{125}$

Thus, the required conditional probability is

$\displaystyle P(B|A)=\frac{\frac{10}{125}}{\frac{24}{125}}$

$\displaystyle P(B|A)=\frac{10}{24}=\frac{5}{12}=0.42$

The probability is 42%