Question

A and B are independent events. Which equation below must be true?

A. P(A) = P(B)
B. P(A | B) = P(A)
C. P(A ∩ B) = P(A)
D. P(B) = P(A | B)

Answer 1

Answer with Step-by-step explanation:

A and B are independent events.

Then, we have to find,which equation below must be true.

A. P(A) = P(B)

No, this is not true, example

A: Occurence of 1 in rolling a die P(A)=1/6

B: occurence of an even number on rolling a die P(B)=1/2

B. P(A | B) = P(A)

This is true

since, P(A|B)+P(A)/P(A∩B) and, P(A∩B)=P(A)P(B)

C. P(A ∩ B) = P(A)

This is not true

since, P(A∩B)=P(A)×P(B)

D. P(B) = P(A | B)

This is not true

Answer 2

The correct answer for this question is B. P(A | B) = P(A). Another equation used for independent events is P(B | A) = P(B). When the multiplication rule is applied, this gives an alternative definition of independence which is:

P(A ∩ B) = P(A)*P(B)

Independent events are events that can occur without affecting or changing the probability of the other.