If two unbiased six-faced dice are thrown simultaneously until a sum of either 7 or 11 occurs, then the probability that 7 comes before 11 is

Step-by-step solution

Consider A and B be the events when the sum is obtained as 7 and 11 respectively. Number of times sum   7 and 11 occur are, n ( A ) = ( 2 , 5 ) , ( 5 , 2 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 1 , 6 ) , ( 6 , 1 ) = 6 n ( B ) = ( 5 , 6 ) , ( 6 , 5 ) = 2 Now, the probability is, P ( A ) = 6 36 = 1 6 P ( B ) = 2 36 = 1 18 The probability when neither the sum of   7   or 11 occurs, P C = 36 - ( 6 + 2 ) 36 = 7 9 The probability that   7 comes before 11 , P = 1 6 + 1 6 × 7 9 + 7 9 2 1 6 + 7 9 3 1 6 &#8230