Question

Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.

Answer 1

$\displaystyle \frac{175}{1296}$

Answer 2

Step 1: Interpret “highest number is 4”
This means all dice show a number ≤ 4, and at least one die shows 4.

Step 2: Use complementary counts

• Total outcomes: $6^4$.
• Outcomes with all faces ≤ 4: $4^4$.
• Outcomes with all faces ≤ 3: $3^4$.

So

P(\max=4) = \frac{\text{#(all ≤4)} - \text{#(all ≤3)}}{6^4} = \frac{4^4 - 3^4}{6^4} = \frac{256 - 81}{1296} = \frac{175}{1296}.