Question

During the past five years the probability that a California consumer has bought a burrito (event B) is 0.70 and the probability that a California consumer has bought a Honda (event H) is 0.10.

The probability that a California consumer has bought both a burrito and and Honda in the past five years is 0.05.

Are the purchases of burritos and Hondas in the past five years among California consumers independent events?

No, they are not independent events.

The reason your answer to the question above is correct is:

A. P(B)−P(H)>P(B∪H)

B. P(B∪H)=P(B)+P(H)−P(B∩H)

C. P(B∣H)≠P(B)

D. P(H)⋅P(B)=P(H∩B)

E. P(H∣B)=P(H)

Answer 1

Here because as we are given that p(H intersection B ) not equal to p(H).p(B)

So, both are not independent

That's why p(H | B) not equal to p(B)

Because p(H|B) = p( H intersection B)/p(B)

Option C