Question

A die is thrown twice. What is the probability that

(i) 5 will not come up either time?

(ii) 5 will come up at least once? 

[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

Answer 1

Outcomes= (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1)(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)

(i) P(5 will not come up either time) = 25/36

Explanation:- 5 will not come up either time means In the throw no dice gets a number 5 on them so possible outcomes = (1,1),(1,2),(1,3),(1,4),(1,6)

(2,1)(2,2),(2,3),(2,4),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,6)

(6,1),(6,2),(6,3),(6,4),(6,6)

(ii) P(5 will come up at least once) = 11/36

Explanation:- 5 will come up at least once means either of the dice gets a number 5 on them. So possible outcomes are :- (1,5),(2,5),(3,5),(4,5),(6,5) (5,1),(5,2),(5,3),(5,4),(5,5),(5,6)