Multiple choice

The least number of times a fair coin must be tossed so that the probability of getting atleast one head is $0.8$, is

  1. $7$
  2. $6$
  3. $5$
  4. $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P(at least one head) = 1 - P(no heads) = 1 - (1/2)^n = 0.8. (1/2)^n = 0.2. 2^n = 5. Since 2^2 = 4 and 2^3 = 8, n must be at least 3.

AI explanation

The probability of getting at least one head in n tosses is found by subtracting the probability of getting all tails from 1, giving the formula 1 - (1/2)^n >= 0.8. Solving this yields (1/2)^n <= 0.2. Testing n=3 gives 1/8, which is 0.125, and since 0.125 is less than 0.2, n=3 is the minimum number of tosses required.

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