Multiple choice

A fair coin is tossed $6$ times. What is the probability of getting at least $3$ heads?

  1. $\cfrac{11}{16}$
  2. $\cfrac{21}{32}$
  3. $\cfrac{1}{18}$
  4. $\cfrac{3}{64}$
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B Correct answer
Explanation

The probability of getting at least 3 heads in 6 tosses is calculated using the binomial distribution formula. The total outcomes are 2^6 = 64. The number of ways to get 3, 4, 5, or 6 heads is 20 + 15 + 6 + 1 = 42. Thus, the probability is 42/64 = 21/32.

AI explanation

The total number of outcomes is 2 to the power of 6, which is 64. The probability of getting at least 3 heads is the sum of the probabilities of getting 3, 4, 5, or 6 heads, calculated as (20 plus 15 plus 6 plus 1) divided by 64. This equals 42 divided by 64, which simplifies to 21/32. The result is 21/32.

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