1.

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

Answer»

We have, a sample space associated with an experiment is 

S = {(x, y): x = 1,6 and 

y = 1.2,3,4,5,6} 

= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (6,2), (6,3), (6,4), (6,5), (6,6)} 

∴ n(S) = 12 

(i) Let A: ‘sum of the numbers that turn up is 3’ 

∴ A = {(1,2)} ∵ 1 + 2 = 3 

⇒ n(A) = 1 

∴ Required probability

= P(A) = n(A)/n(S) = 1/12

 (ii) Let B: ‘sum of the numbers that turn up is 12’. 

⇒ B = {(6,6)} ∵ 6 + 6 = 12 

∴ Required probability

= P(B) = 1/12 = n(B)/n(S)


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