Two dice are thrown simultaneously. What is the probability that the sum of numbers on the two faces is divisible by 4 or 6?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{7}{18}\)
Two dice give \(6\times6=36\) equally likely outcomes. Sums “divisible by 4 or 6” are counted by adding the two groups and taking off the sum that is in both groups (12), so that it is not counted twice.
Sums divisible by 4:
sum 4: (1, 3), (2, 2), (3, 1) — 3 ways
sum 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) — 5 ways
sum 12: (6, 6) — 1 way
Sums divisible by 6:
sum 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) — 5 ways
sum 12: (6, 6), already counted above
Favourable outcomes and the probability:
Favourable outcomes, the 12 counted once: \(3+5+1+5=14\)
Probability \(=\) favourable \(\div\) total \(=\displaystyle\frac{14}{36}=\frac{7}{18}\)
Tip: In an “A or B” count, look for the outcome that is in both groups (here the sum 12) and count it only once; adding 9 and 6 to get 15 is the usual slip.