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Nov 2021 p52 q1
2584
Each of the 180 students at a college plays exactly one of the piano, the guitar, and the drums. The numbers of male and female students who play the piano, the guitar, and the drums are given in the following table.
Piano
Guitar
Drums
Male
25
44
11
Female
42
38
20
A student at the college is chosen at random.
Find the probability that the student is male given that the student plays the drums.
Solution
To find the probability that a student is male given that they play the drums, we use conditional probability:
\(P(M \mid D) = \frac{P(M \cap D)}{P(D)}\)
From the table, the number of male students who play the drums is 11. The total number of students who play the drums is 11 (male) + 20 (female) = 31.
Thus, \(P(M \cap D) = \frac{11}{180}\) and \(P(D) = \frac{31}{180}\).