Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is at least 23 ?

Step-by-step solution

Total number of outcomes when four dice are rolled is 6^4 = 1296 . Let x₁, x₂, x₃, x₄ be the numbers on the four dice. The required condition is x₁ + x₂ + x₃ + x₄ 23 . Since the maximum possible sum is 24 , the possible values for the sum are 23 and 24 . For the sum to be 24 , all four dice must show 6 . Number of ways = 1 For the sum to be 23 , three dice must show 6 and one die must show 5 . Number of ways = 4! 3!1! = 4 Total number of favorable outcomes = 1 + 4 = 5 . Required probability = 5 1296 . Answer: 5 129