Multiple choice

A die is thrown four times and the sum of the numbers is noted. If the sum of the numbers is 23 then the probability is

  1. 1/324

  2. 1/342

  3. 1/243

  4. 1/322
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A Correct answer
Explanation

The sum of 4 dice is 23. The only combinations are (6,6,6,5) in 4 permutations. Total outcomes are 6^4 = 1296. Probability = 4/1296 = 1/324.

AI explanation

The total number of outcomes when a die is thrown four times is 6^4, which equals 1296. To get a sum of 23, the four outcomes must be 6, 6, 6, 5 in any order, and there are 4C1 or 4 ways to arrange these numbers. The probability is the number of favorable outcomes divided by the total outcomes, which is 4/1296. Simplifying this fraction by dividing the numerator and the denominator by 4 gives a probability of 1/324.

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