An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2 , 3 , … , 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is

Step-by-step solution

Let, A be the event that the noted number is either 7 or 8 . And, E 1 be the event that the toss of coin results in head and E 2 be the event that the toss of coin results in tail. Then, we have P E 1 = P E 2 = 1 2 And, P A | E 1 = P ( getting the sum of the numbers on the pair of dice as 7 or 8 ) The total number of cases, when a pair of dice is thrown are = 6 × 6 = 36 and the cases of getting sum 7 or 8 are 1 ,   6 ,   2 ,   5 ,   3 ,   4 ,   4 ,   3 ,   5 ,   2 ,