Question

What is the probability that when a pair of dice is rolled, at least one die shows a 3 or the dice sum to 8?

Answer 1

Answer: P(3 or 8) = 7/18

Step-by-step explanation:

Each dice has 6 faces, so there are 36 possibilities in 2 dice.

Possibilities of them sum to 8: (2,6) (3,5) (4,4) (5,3) (6,2);

Probability of it happening: P(sum 8) = P(A) = 5/36

Possibilities of one die shows a 3: (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (3,1) (3,2) (3,4) (3,5) (3,6)

Probability of it happening: P(3) = P(B) = 11/36

Possibilities that happen at the same time: (3,5) (5,3)

Probability of happening: P(A∩B) = 2/36

The 'or' probability is to add the events and subtract the probabilities thata happens at the same time:

P(3 or sum 8) = P(A) + P(B) - P(A∩B)

P(3 or sum 8) = 5/36 + 11/36 - 2/36

P(3 or sum 8) = 14/36 = 7/18

Answer 2

Given condition is that two die are rolled together. So there are 36 combinations of two rolled dice. And the following have a sum of 8 : 2–6, 3–5, 4–4, 5–3 and 6–2. Out of these five combinations, 2 show the number 3.

So probability(sum is 8) becomes = $\frac{5}{36}$

And probability of (shows a number 3) becomes = $\frac{2}{36}$