Multiple choice

Gurkiran has 9 five rupee coins with her. What is the probability that she obtains at least five heads, when she tosses each coin once?

  1. 5/9

  2. 4/9

  3. 1/2

  4. 2/9
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C Correct answer
Explanation

This is a binomial distribution problem with n=9, p=0.5. Probability of at least 5 heads is P(X>=5). Since the distribution is symmetric, P(X>=5) = P(X<=4). P(X>=5) + P(X<=4) = 1. 2*P(X>=5) = 1, so P(X>=5) = 0.5.

AI explanation

When tossing 9 coins, the probability of getting exactly k heads is given by the binomial distribution formula, which is 9Ck divided by 2^9. The probability of obtaining at least five heads is the sum of the probabilities for 5, 6, 7, 8, and 9 heads. Calculating this sum gives (126 + 84 + 36 + 9 + 1) / 512 = 256/512, which equals 1/2.

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