Multiple choice

A coin is tossed n times. If the probability of getting at least one head is atleast $99\%$, then the minimum value of n is?

  1. $6$
  2. $7$
  3. $8$
  4. $9$
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. We need 1 - (1/2)^n >= 0.99, which simplifies to (1/2)^n <= 0.01. Since (1/2)^6 = 1/64 = 0.0156 and (1/2)^7 = 1/128 = 0.0078, the minimum n is 7.

AI explanation

The probability of getting no heads in n tosses is one half to the power of n, so the probability of getting at least one head is 1 minus one half to the power of n. For this probability to be at least 99 percent, or 0.99, we set 1 minus one half to the power of n greater than or equal to 0.99. This simplifies to one half to the power of n being less than or equal to 0.01, meaning 2 to the power of n must be at least 100. Since 2 to the power of 6 is 64 and 2 to the power of 7 is 128, the minimum value of n is 7.

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