Multiple choice

A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.

  1. $\dfrac { 5 }{ 36 } $
  2. $\dfrac { 5 }{ 16 } $
  3. $\dfrac { 6 }{ 11 } $
  4. $\dfrac { 1 }{ 6 } $
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B Correct answer
Explanation

This is a binomial distribution problem with n=5, p=1/2 (odd numbers on a die are 1, 3, 5). P(X=3) = 5C3 * (1/2)^3 * (1/2)^2 = 10 * (1/32) = 10/32 = 5/16.

AI explanation

Using the binomial distribution formula, the probability of exactly r successes in n trials is nCr * (p)^r * (q)^(n-r). The probability of rolling an odd number is p = 3/6 = 1/2, and the probability of an even number is q = 1/2. For exactly 3 odd numbers in 5 throws, the calculation is 5C3 * (1/2)^3 * (1/2)^2 = 10 * (1/8) * (1/4) = 10/32 = 5/16.

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