Multiple choice

Two dice are thrown simultaneously What is the probability of getting two numbers whose product is even?

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{3}{4}$
  3. $\displaystyle \frac{3}{8}$
  4. $\displaystyle \frac{5}{16}$
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B Correct answer
Explanation

The product of two numbers is odd only if both numbers are odd. The probability of one die being odd is 1/2. The probability of both being odd is 1/2 * 1/2 = 1/4. The probability of the product being even is 1 - P(odd) = 1 - 1/4 = 3/4.

AI explanation

For two rolled dice, the product of the numbers is odd only when both numbers are odd, which happens in 3 multiplied by 3, or 9, ways. Using the complement method, the probability of an even product is 1 minus the probability of an odd product. This is calculated as 1 minus 9/36, which is 27/36. Simplifying the fraction gives 3/4.

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