# 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. - Mathematics

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.

#### Solution

Solution:
The total number of outcomes when two dice are tossed together is 36.
The sample space is as follows

 1 2 3 4 5 6 1 (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 E be the event ‘that 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) }
Probability that the number on each dice is even P(E)

="Number of favourable outcomes"/"Total number of outcomes"=9/36=1/4

ii. Let F be the event
iii. Favourable outcomes = { (1,4) (2,3) (3,2) (4,1) }
Probability that the sum of the numbers appearing on the two dice is 5

="Number of favourable outcomes"/"Total number of outcomes"4/36=1/ 9

Concept: Basic Ideas of Probability
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