A night before an exciting cricket clash between the 2 teams, the captains of the two teams got the same idea and decide to check their luck by tossing coins, so that they get an edge over the other at the toss. If both tossed 4 coins each, the probability that they both end up with same number of heads is?
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Possibilities and probabilities tossing 4 coins are:
to get 0 heads probability is 2 4 1 , for two persons 2 4 1 ⋅ 2 4 1 = 2 5 6 1
to get 1 head is 2 4 ( 1 4 ) , for two persons 1 6 4 ⋅ 1 6 4 = 2 5 6 1 6
to get 2 heads is 2 4 ( 2 4 ) , for two persons 1 6 6 ⋅ 1 6 6 = 2 5 6 3 6
to get 3 heads is 2 4 ( 3 4 ) , for two 1 6 4 ⋅ 1 6 4 = 2 5 6 1 6
to get 4 heads is 2 4 1 , for two 1 6 1 ⋅ 1 6 1 = 2 5 6 1
Sum of these probabilities is 2 5 6 7 0 = 1 2 8 3 5