Question

Two fair dice are rolled:

a) What is the probability of an even number or a 3 on the first die? Are these two events mutually exclusive and why?

b) What is the probability of an even number on the first die and a 5 on the second? Is conditional probability involved in this case? Why or why not?

Answer 1

If two fair dice are rolled , then there are total 6*6 = 36 outcomes

a) P( even number or 3 on the first die )

So there are 24 outcomes such that even number or 3 on the first die

P( even number or 3 on the first die ) = 24/36 = 0.6667

Two events A and B are mutually exclusive if they do not have common outcome or they can't occur at a same time

So for mutually exclusice events ,P( A and B ) = 0

Let here A be event that even number of first die and B be the event that 3 on the first die

Both event can not occur at a same time , so both are mutually exclusive events.

b) P( even number on first die and 5 on second )

Let A be event that even number of first die and B be the event that 5 on second

There are 3 outcomes for such event

P( even number on first die and 5 on second ) = P ( A and B ) = 3/36 = 0.0833

Conditional probability can be involved in this case , because A and B are depenent events

For dependent events ,

P( A | B ) =  P ( A and B ) / P(B)

OR P( B | A ) =  P ( A and B ) / P(A)