Question

A dice is rolled twice and sum of numbers is observed.

(i) What is the probability that the number 4 has occurred on one of the dice, if the sum is 6? 

(ii) What is the probability that the number 3 has occurred on one of the dice, if the sum is 4?

Answer 1

A dice is rolled twice. So no. Of elements in sample space = 36

 i.e. {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)(2,1),........(6,6)}

1) sum = 6 and 4 has occurred on one of dice= {(2,4),(4,2)}

Probability= Possible outcome/Total outcome = 2/36

= 1/18

2) 3 has occurred one of dice and sum 4 cases = {(1,3),(3,1)}

Probability = 2/36

= 1/18