Passage: Four dice are rolled. Question: What is the probability...

Total number of outcomes when four dice are rolled is $6^4 = 1296$.

Let $x_1, x_2, x_3, x_4$ be the numbers on the four dice. The required condition is $x_1 + x_2 + x_3 + x_4 \ge 23$.

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 = $\dfrac{4!}{3!1!} = 4$

Total number of favorable outcomes = $1 + 4 = 5$.

Required probability = $\dfrac{5}{1296}$.

Answer: $\dfrac{5}{1296}$