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Question:

Two different dice are tossed together. Find the probability (i) that the number on each die is even. (ii) that the sum of numbers appearing on the two dice is 5.

i)15and ii)16

i)13and ii)18

i)12and ii)17

i)14and ii)19

Solution:

123456
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
2(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
3(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
4(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
5(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
6(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
(i) Let the event that the number of each die is even.
Favourable outcomes=(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)
Probabaility that number on each dice is even=9/36=1/4
(ii) That the sum of numbers appearing on the two dice is 5.
Favourable outcomes=(1,4),(2,3),(3,2),(4,1)
Probability that the sum of the numbers appearing on the two dice is 5=4/36=1/9