Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{7}{18}\)
Two dice give \(6\times6=36\) equally likely outcomes, with sums from 2 to 12. The sums divisible by 4 or 6 are 4, 6, 8 and 12; 12 is divisible by both, so it is counted only once.
Sum 4: (1, 3), (2, 2), (3, 1), 3 outcomes
Sum 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), 5 outcomes
Sum 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), 5 outcomes
Sum 12: (6, 6), 1 outcome
Favourable outcomes: \(3+5+5+1=14\), so the probability is \(\displaystyle\frac{14}{36}=\frac{7}{18}\)
Tip: Counting (6, 6) twice, once for 4 and once for 6, gives \(\frac{15}{36}=\frac{5}{12}\), Option (1); an outcome that fits both conditions is counted once.