A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is m n , (m, n) = 1 , then m + n is equal to:

Step-by-step solution

Let h be the number of heads and t be the number of tails obtained. The total points obtained is 10h + 5t . For the man to get exactly 30 points, we must have: 10h + 5t = 30 2h + t = 6 Since h and t are non-negative integers, the possible pairs of (h, t) are (3, 0) , (2, 2) , (1, 4) , and (0, 6) . For each pair, the number of possible sequences of heads and tails is given by ^ h+t C_ h , and the probability of any specific sequence is ( 1 2 )^ h+t . The total probability is the sum of the probabilities of all these