Question

A dice is rolled twice. Find the probability that
(i) 5 will not come up either time.
(ii) 5 will come up exactly one time

Answer 1

A dive is rolled twice then

total 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)

total outcomes-=36

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

(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)

total possible outcomes-25

P(5 will not come up either time) = total no.of possible outcomes/no. of outcomes

=25/36

(ii) P(5 will come up exactly one time) =

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

total possible outcomes=9

P(5 will come up exactly one time) = 9/36=1/4