Multiple choice

If a fair coin is tossed 10 times the probability of at least 6 heads is

  1. 105/512

  2. 53/128

  3. 53/64

  4. 193/512
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D Correct answer
Explanation

The probability of at least 6 heads in 10 tosses is P(X >= 6) = P(6) + P(7) + P(8) + P(9) + P(10). Using the binomial formula (10 choose k) * (1/2)^10: (210 + 120 + 45 + 10 + 1) / 1024 = 386 / 1024 = 193 / 512.

AI explanation

Using the binomial distribution formula, the probability of at least 6 heads in 10 tosses is the sum of the probabilities of getting exactly 6, 7, 8, 9, and 10 heads. The favorable outcomes are calculated as 10C6 + 10C7 + 10C8 + 10C9 + 10C10, which equals 210 + 120 + 45 + 10 + 1 = 386. Since the total possible outcomes are 2^10 = 1024, the probability is 386/1024, which simplifies to 193/512.

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