Multiple choice

In order to get a heat at least once with probability $\ge 0.9$, the minimum number of times a unbiased coin needs to be tossed is

  1. $3$
  2. $4$
  3. $5$
  4. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of getting at least one head in n tosses is 1 - (1/2)^n. For 3 tosses this is 7/8, which is below 0.9, while 4 tosses gives 15/16, which is at least 0.9.

AI explanation

The probability of getting no heads in n tosses is (1/2)^n, so the probability of getting at least one head is 1 - (1/2)^n. For n = 3, the probability is 1 - 1/8 = 0.875, which is less than 0.9. For n = 4, the probability is 1 - 1/16 = 0.9375, which is greater than 0.9. The minimum number of tosses required is 4. The result is 4.

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