A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

Step-by-step solution

Let X be the number of successful predictions, which corresponds to the number of heads obtained in 9 tosses. The number of unsuccessful predictions is 9 - X . The condition that the number of successful predictions is strictly greater than the number of unsuccessful predictions is X > 9 - X , which gives 2X > 9 , or X 5 . Since the coin is fair, the probability of getting heads is p = 1 2 and tails is q = 1 2 . The probability of getting exactly r heads is P(X = r) = ⁹C_ r ( 1 2 )⁹ . The required probability is P(