Question

John and Paul play the following game. They each roll one fair 6-sided die. John wins
the game if his score is larger than Paul’s score or if the product of the scores is an odd number.

Find the probability that John wins.

Answer 1

John and Paul each roll one fair sided die.

So all possible outcome 6²=36

Let us define the events,

A= John's score is larger than Paul's score.

Sample space= { ( 2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)}

So, P(A) =15/36

B=product of the scores is an odd number

Sample space of B={(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}

So, P(B) = 9/36

Now A B = {(3,1),(5,1),(5,3)}

Now P(A B ) = 3/36

Now given that John wins if event A or event B happened

So, P(John wins) = P (A U B)

= P( A)+ P ( B) - P (A B )

= 15/36+9/36- 3/36

=(24-3)/36 = 21/36 = 0.58

The probability that John wins is 0.58