Multiple choice

If a coin is tossed 3 times the probability of obtaining 2 heads or 2 tails is

  1. $\dfrac{1}{4}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{3}{4}$
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D Correct answer
Explanation

Total outcomes for 3 coin tosses = 2^3 = 8. Outcomes with 2 heads: HHT, HTH, THH (3). Outcomes with 2 tails: TTH, THT, HTT (3). Total favorable outcomes = 3 + 3 = 6. Probability = 6/8 = 3/4.

AI explanation

When a coin is tossed 3 times, there are 2^3 = 8 total possible outcomes. The number of outcomes with exactly 2 heads is 3C2 = 3, and the number of outcomes with exactly 2 tails (which means exactly 1 head) is 3C1 = 3. Using the addition rule for mutually exclusive events, the total favorable outcomes are 3 + 3 = 6. The probability is 6/8, which simplifies to 3/4.

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