Quantitative: Permutations, Combinations & Probability
Subtopic: Probability of dice roll sum
Question Statement:
Two unbiased six-faced dice are rolled simultaneously. The probability that the sum of the numbers appearing on the two dice equals $7$ is ________ (round off to four decimal places).
Answer Key:
0.1667
Step-by-Step Solution & Explanation
Total possible outcomes $N = 6 \times 6 = 36$.
Favorable outcomes giving sum $7$ are: $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$, total $n = 6$.
$P(\text{sum} = 7) = \frac{6}{36} = \frac{1}{6} \approx 0.1667$