Question 20 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 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? A. 0.12 B. 0.74 C. 0.26 D. 0.48
Question 20 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 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? A. 0.12 B. 0.74 C. 0.26 D. 0.48
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Question 20 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 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?
- A. 0.12
- B. 0.74
- C. 0.26
- D. 0.48
**Explanation:**
To find the probability that a randomly selected band member is in the brass section and plays trombone, multiply the probability of being in the brass section by the probability of playing trombone given that they are in the brass section.
Calculation:
\[ P(\text{Brass and Trombone}) = P(\text{Brass}) \times P(\text{Trombone | Brass}) \]
\[ P(\text{Brass and Trombone}) = 0.50 \times 0.24 = 0.12 \]
Therefore, the correct answer is A. 0.12.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79765f1f-1ae4-4441-a1ec-ee9ddafb1901%2Fffcead59-0c8a-4b6b-a8f9-d7eb94a25999%2Fdl7t7it_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 20 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 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?
- A. 0.12
- B. 0.74
- C. 0.26
- D. 0.48
**Explanation:**
To find the probability that a randomly selected band member is in the brass section and plays trombone, multiply the probability of being in the brass section by the probability of playing trombone given that they are in the brass section.
Calculation:
\[ P(\text{Brass and Trombone}) = P(\text{Brass}) \times P(\text{Trombone | Brass}) \]
\[ P(\text{Brass and Trombone}) = 0.50 \times 0.24 = 0.12 \]
Therefore, the correct answer is A. 0.12.
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