Two dice are thrown simultaneously. What is the probability that the sum of the number appearing on the dice is
(i) 7 (ii) a prime number (iii) 1

Explanation

Two dice are thrown simultaneously
So, total number of possible outcomes=36
(i) Sum of the number appearing on the dice is 7.
So, the possible ways are (1,6),(2,5),(3,4),(4,3),(5,2) and (6,1)
Number of possible ways=6
`therefore` Required probability=`(6)/(36)=(1)/(6)`
(ii) Sum of the numbers appearing on the dice is a prime number i.e. 2,3,5,7 and 11
So, the possible ways are (1,1), (1,2), (2,1), (1,4), (2,3),(3,2), (4,1), (1,6), (2,5),(3,4),(4,3),(5,2),(6,1),(5,6) and (6,5)
Number of possible ways=15
`therefore` "Required probability=(15)/(36)=(5)/(12)`
(iii) Sum of the number appearing on the dice is 1.
It is not possible, so its probability is zero.