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In a concert band, a the probability that a member is in the brass section is
0.50. The probability that a member plays trombone, given that he or she is in
the brass section, is 0.24.
What is the probability that a randomly selected band member is in the brass
section and plays trombone?
O A. 0.74
• B. 0.48
• C. 0.26
• D. 0.12

Respuesta :

Using conditional probability, the probability that a randomly selected band member is in the brass section and plays trombone is:

D. 0.12

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

For this problem, the events are:

  • Event A: Student in the brass section.
  • Event B: Student plays trombone.

Hence the parameters are:

P(A) = 0.5, P(B|A) = 0.24.

The probability of both events is found as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.24 \times 0.5 = 0.12[/tex]

Hence option D is correct.

More can be learned about conditional probability at https://brainly.com/question/24372153

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