Multiple choice

A fair coin is tossed $4$ times. The probability that head exceed tail in numbers is

  1. $\dfrac{3}{16}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{5}{16}$
  4. $\dfrac{7}{16}$
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C Correct answer
Explanation

With 4 coin tosses, there are 2^4 = 16 total outcomes. Heads exceed tails if there are 3 heads (4C3 = 4 ways) or 4 heads (4C4 = 1 way), totaling 5 favorable outcomes. Thus, the probability is 5/16.

AI explanation

For heads to exceed tails in 4 tosses, there must be either exactly 3 heads or exactly 4 heads. Using the binomial probability formula, the probability of exactly 3 heads is 4C3 times (1/2)^3 times (1/2)^1, which equals 4/16. The probability of exactly 4 heads is 4C4 times (1/2)^4, which equals 1/16. Adding these probabilities gives 5/16.

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