Multiple choice

A fair coin is tossed $4$ times. Then the probability of getting one time head and $3$ times tail is:

  1. $\dfrac14$
  2. $\dfrac34$
  3. $\dfrac12$
  4. $\dfrac38$
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A Correct answer
Explanation

Total outcomes = 2^4 = 16. Favorable outcomes (1H, 3T) = 4C1 = 4. Probability = 4/16 = 1/4.

AI explanation

Using the binomial probability formula, the probability of exactly k successes in n trials is (n choose k) times p to the power of k times q to the power of (n minus k). Here, n is 4, k is 1, and the probability of heads p is 1/2. The calculation is 4 factorial divided by (1 factorial times 3 factorial) times 1/2 to the power of 1 times 1/2 to the power of 3, which equals 4 times 1/16, giving a final probability of 1/4.

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