Suppose that a high school marching band has 125 members. Of these 125 band members, 41 are seniors, 24 play the trumpet, and 10

Question

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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

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-04-08T07:53:44+03:00

Response:

The likelihood is 42%

Detailed explanation:

Conditional Probability

This measures the chance of event B happening given that event A has occurred and that A and B are associated (not independent).

If P(A) signifies the chance of A occurring, $P(A\cap B)$ represents the probability of both events happening, and P(B|A) denotes the sought probability of B's occurrence:

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

We know that there are 125 members in the high school marching band, with 41 being seniors (event B), 24 playing the trumpet (event A), and 10 seniors who also play the trumpet.

The chance a randomly chosen band member plays the trumpet is

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

The chance that this individual possesses both characteristics is

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

Therefore, the conditional probability required 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 likelihood is 42%