Multiple choice

On tossing a fair coin for $5$ times, what is the probability that at least four of the five flips will be heads?

  1. $\cfrac{3}{16}$
  2. $\cfrac{3}{10}$
  3. $\cfrac{7}{10}$
  4. $\cfrac{13}{16}$
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A Correct answer
Explanation

Binomial distribution: n=5, p=0.5. P(X >= 4) = P(X=4) + P(X=5) = (5C4 * (0.5)^5) + (5C5 * (0.5)^5) = (5 + 1) / 32 = 6 / 32 = 3/16.

AI explanation

The probability of getting a head on a fair coin is 1/2, and the total number of outcomes for 5 flips is 2^5 = 32. Using the binomial probability formula for getting exactly 4 heads (5C4 times (1/2)^5) gives 5/32, and for exactly 5 heads (5C5 times (1/2)^5) gives 1/32. Adding these probabilities gives (5/32) + (1/32) = 6/32, which simplifies to 3/16.

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