Question

An experiment consists of rolling two dice, let E1= “The sum of the numbers is greater than 7” and E3= “The numbers on the two dice are equal”.

a. Are E1 and E3 mutually exclusive?

b. What are the odds of rolling a pair with the same number on the faces?

Answer 1

a) No, since there are outcomes where sum is greater than 7 and number on both dies are equal , such as if both dice show 4, then sum is 8 which is even as well greater than 7.

b)

P(getting same number on both dice) =6/36 =1/6 (since 6 such outcome)

therefore odds =probability/(1-probabilty) =(1/6)/(1-1/6 )=1/5 or 1 to 5