Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is:

Step-by-step solution

Each of the persons A and B independently tosses three fair coins. Let X be the number of heads obtained by A and Y be the number of heads obtained by B . Both X and Y are binomial variate with parameters, n = 3   &   p = 1 2 Probability that both A and B obtain the same number of heads = P X = 0 P Y = 0 + P X = 1 P Y = 1 + P X = 2 P Y = 2 + P X = 3 P Y = 3 = C 0 3   1 2 3 2 + C 1 3   1 2 3 2 + C 2 3   1 2 3 2 + C 3 3   1 2 3 2 = 1 ×   1 2 3 2 + 3 ×   1 2 3 2 +