Four fair dice are thrown together. What is the probability that all four dice show the same number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{216}\)
Each die can show any of 6 numbers, so four dice give \(6^4\) equally likely outcomes. All four agree only in the 6 outcomes where every die shows 1, or every die shows 2, and so on up to 6.
Total outcomes \(=6\times6\times6\times6=1296\)
Favourable outcomes: (1, 1, 1, 1), (2, 2, 2, 2), …, (6, 6, 6, 6), that is 6
Probability \(\displaystyle =\frac{6}{1296}=\frac{1}{216}\)