Question

The probability that comic book reader in a particular city prefers comics published by company A is 25%. The probability that comic book reader in the city's is male 70%

Answer 1

Complete question is;

The probability that a comic book reader in a particular city prefers comics published by Company A is 25%. The probability that a comic book reader in the city is male is 70%. If the probability of a comic book reader in the city being a male, given that the reader prefers Company A's comics, is 40%, what is the probability of the reader preferring Company A's comics, given that the reader is a male?

Answer:

0.14 or 14%

Step-by-step explanation:

We are told that the probability that the comic book readers prefers comics published by company A is 25%.

Thus; P(A) = 25% = 0.25

Also, we are told that the probability that comic book reader is male 70%.

Thus; P(M_r) = 70% = 0.7

We are also told that the probability of a comic book reader being a male, provided that the reader prefers Company A's comics, is 40%.

Thus; P(A|M_r) = 40% = 0.4

To find the probability of the reader preferring Company A's comics, provided that the reader is a male, we will apply baye's theorem.

Thus;

P(M_r|A) = [P(A|M_r) × P(A)]/P(M)

P(M_r|A) = (0.4 × 0.25)/0.7

P(M_r|A) ≈ 0.14