Multiple choice

A coin is tossed $n$ times. The maximum value of $n$ such that the probability of getting no head is greater than $1/16$ is

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

The probability of getting no heads in n tosses is (1/2)^n. We need (1/2)^n > 1/16. This means 2^n < 16. The values of n satisfying this are 1, 2, and 3. The maximum is 3.

AI explanation

The probability of getting no heads in n tosses is (1/2) to the power of n. Testing the options, if n equals 4, the probability is 1/16, which is not strictly greater than 1/16; however, if n equals 3, the probability is 1/8. Since 1/8 is greater than 1/16 and any larger value of n yields a probability less than or equal to 1/16, the maximum value is 3.

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