Multiple choice

A person throws two dice, one the common cube and the other a regular tetrahedron, the number on the lowest face being taken in the case of the tetrahedron. What is the chance that the sum of the numbers thrown is not less than 5?

  1. $\displaystyle \frac{18}{24}=\frac{3}{4}$
  2. $\displaystyle \frac{6}{24}=\frac{1}{4}$
  3. $\displaystyle \frac{6}{18}=\frac{1}{3}$
  4. $\displaystyle \frac{12}{18}=\frac{2}{3}$
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A Correct answer
Explanation

A cube has 6 faces (1-6). A tetrahedron has 4 faces (1-4). Total outcomes = 6 * 4 = 24. Sum < 5: (1,1), (1,2), (1,3), (2,1), (2,2), (3,1). Total 6 outcomes. Sum >= 5 = 24 - 6 = 18. Probability = 18/24 = 3/4.

AI explanation

The total number of possible outcomes is the product of the 6 faces of the cube and the 4 faces of the tetrahedron, giving 24 outcomes. To find the outcomes where the sum is less than 5, the favorable pairs are (1,1), (1,2), (1,3), (2,1), (2,2) and (3,1), totaling 6 outcomes. The probability of the sum being not less than 5 is found by subtracting the probability of the sum being less than 5 from 1, giving 1 minus (6 divided by 24), which equals 18/24 or 3/4.

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