Multiple choice

What is the minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.95?

  1. 2

  2. 3

  3. 5

  4. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting at least one head in n tosses is 1 - (1/2)^n. We need 1 - (1/2)^n > 0.95, which means (1/2)^n < 0.05. For n=4, (1/2)^4 = 0.0625. For n=5, (1/2)^5 = 0.03125. Thus, 5 tosses are required.

AI explanation

The probability of not getting any heads in n tosses is (1/2)^n, so the probability of at least one head is 1 - (1/2)^n. Setting this greater than 0.95 gives (1/2)^n < 0.05. Testing n = 5 gives 1/32 = 0.03125, which is less than 0.05, while n = 4 gives 1/16 = 0.0625, which is not. Therefore, the minimum number of tosses required is 5.

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