Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99%

Let n be the number of times a fair coin is tossed. The probability of getting at least one head is given by 1 - P(no heads). The probability of getting no heads (all tails) in n tosses is (1/2)^n. Therefore, the probability of getting at least one head is 1 - (1/2)^n. We want this probability to be greater than 0.99. So we have the inequality: 1 - (1/2)^n > 0.99 This simplifies to: (1/2)^n < 0.01 Taking the reciprocal of both sides and reversing the inequality sign: 2^n > 100 We can test values of n: For n=6, 2^6 = 64 < 100 For n=7, 2^7 = 128 > 100 Therefore, the minimum number of times the coin must be tossed is 7. The correct option is 7