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?

Two dice are thrown simultaneously. What is the probability that the s

1.	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?
Answer» 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.