Multiple choice

An urn contains $25$ balls numbered $1$ through $25$. Suppose getting an odd number is a success. Two balls are drawn from the urn with replacement. The probability of getting at least one success is

  1. $\dfrac{481}{625}$
  2. $\dfrac{312}{625}$
  3. $\dfrac{144}{625}$
  4. $\dfrac{244}{625}$
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A Correct answer
Explanation

Numbers 1-25. Odd numbers: 1, 3, ..., 25 (13 numbers). P(success) = 13/25. P(failure) = 12/25. P(at least one success) = 1 - P(no success) = 1 - (12/25)^2 = 1 - 144/625 = 481/625.

AI explanation

Using the complementary event method, the probability of getting at least one success equals 1 minus the probability of getting zero successes. A success is drawing an odd number, which occurs with a probability of 13/25, making the probability of failure 12/25. Because the draws are with replacement, the probability of getting two failures is (12/25)^2 = 144/625. The required probability of at least one success is 1 - 144/625 = 481/625.

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