Multiple choice

Shawn has 9 one-dollar coins with him. What is the probability of obtaining at least five heads, when he tosses each coin once?

  1. 5 9

  2. 4 9

  3. 1 2

  4. 2 9

  5. 1 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distribution of heads in 9 coin tosses is symmetric. The probability of getting at least 5 heads is equal to the probability of getting at least 5 tails. Since the total probability is 1, and the probability of getting exactly 4.5 heads is impossible, the probability of getting >= 5 heads is exactly 1/2.

AI explanation

Using the binomial probability formula, we calculate the probability of getting at least 5 heads in 9 tosses, which is the sum of the probabilities of getting exactly 5, 6, 7, 8, and 9 heads. The probability is (9C5 + 9C6 + 9C7 + 9C8 + 9C9) / 2^9. This gives (126 + 84 + 36 + 9 + 1) / 512 = 256/512, which simplifies to 1/2.

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