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
