Question

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 1

There exist the same question that has the following choices:
A. 0.14
B. 0.25
C. 0.30
D. 0.45

Probability of comic reader prefer Company A = 25%
Probability of a male comic reader = 70%
Probability of a male comic reader prefer Company A = 40%
Probability of a male comic reader prefer Company A 
The correct answer is letter D. 0.45

Answer 2

Answer:

Probability of the reader preferring Company A's comics, given that the reader is a male -0.14

Step-by-step explanation:

Given : Comic published by Company A =25% ⇒ $P(A)=\frac{25}{100}=0.25$

Probability that a comic book reader is male=70% ⇒ $P(M)=\frac{70}{100}=0.7$

Probability of a comic book reader in the city being a male, given that the reader prefers Company A's comics= 40% ⇒ $P(A/M)=\frac{40}{100}=0.4$

To find : Probability of the reader preferring Company A's comics, given that the reader is a male =$P(M/A)$

Solution : Using Bayes' theorem, which state that

$P(A/B)=\frac{P(B/A)P(A)}{P(B)}$

where, P(A) and P(B) are probabilities of observing A and B.

P(B/A)= is a conditional probability where event B occur and A is true

P(A/B)= also a conditional probability where event A occur and B is true.

Now, applying Bayes' theorem,

$P(M/A)=\frac{P(A/M)P(A)}{P(M)}$

$P(M/A)=\frac{(0.4)(0.25)}{0.7}$

$P(M/A)=\frac{0.1}{0.7}$

$P(M/A)=0.14$

Therefore, Probability of the reader preferring Company A's comics, given that the reader is a male -0.14