Question

A single fair die is rolled. Let events A={2,4}, and B={1,2,5}. Event A is independent with event B. True or False?

Answer 1

TRUE

Explanation:

Event A and event B will be independent if

P(A∩B)=P(A)*P(B)

A={2,4}

B={1,2,5}

There are 6 outcomes when die is rolled.

n(S)=6

A∩B={2}

P(A∩B)=n(A∩B)/n(S)=1/6

P(A)=n(A)/n(S)=2/6=1/3

P(B)=n(B)/n(S)=3/6=1/2

P(A)*P(B)=1/3*1/2=1/6

As,

P(A∩B)=P(A)*P(B)

So, event A and event B are independent.