Multiple choice

The minimum number of times one has to toss a fair coin, so that the probability of observing at least one head is at least 90%, is:

  1. 5

  2. 3

  3. 2

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

Probability of at least one head = 1 - P(no heads). P(no heads) = (1/2)^n. We need 1 - (1/2)^n >= 0.9, so (1/2)^n <= 0.1. For n=3, 1/8 = 0.125. For n=4, 1/16 = 0.0625. Thus, 4 tosses are required.

AI explanation

To find the probability of getting at least one head in n tosses, we use the complement rule by calculating 1 minus the probability of getting all tails, which is 1 minus the fraction 1 divided by 2 to the power of n. We need this probability to be greater than or equal to 90 percent, so we set up the inequality 1 minus 1 divided by 2 to the power of n is greater than or equal to 0.90. Checking the values, for n equals 3, the probability is 0.875, and for n equals 4, the probability is 0.9375. Therefore, the minimum number of tosses required is 4.

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