Question

Two persons A and B have n + 1 and n coins, respectively, which they toss simultaneously. Then the probability that A will have more heads than B is 

(A) 1/2 

(B) > 1/2 

(C) < 1/2 

(D) > 1/3

Answer 1

Answer is (A) 1/2

Let α and β be the number of heads and tails thrown by A respectively, then

α + β = n + 1     (1)

Let γ and δ be the number of heads and tails thrown by B respectively, then

γ + β = n

Required probability is P(α > γ) = P(β > δ) = p

Now,

Therefore,

P = 1/2