Question

Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.

Hint:

For product problems, it is usually easier to find the "odd" case first and subtract from total, since \( \text{odd} \times \text{odd} = \text{odd} \) is the only way to get an odd product.

Answer 1

Step 1: Total Outcomes
When two dice are thrown:
Total outcomes = 6 × 6 = 36

Part (i): Probability of Even Sum
Sum is even when:
• Both numbers are even
• Both numbers are odd

Odd numbers = {1, 3, 5} → 3 choices
Even numbers = {2, 4, 6} → 3 choices

Both odd:
3 × 3 = 9 outcomes

Both even:
3 × 3 = 9 outcomes

Total favourable outcomes:
9 + 9 = 18

Probability (even sum) = 18 / 36
= 1/2

Part (ii): Probability of Even Product
Product is even if at least one die shows an even number.

Product is odd only when both dice show odd numbers.

Odd product cases:
3 × 3 = 9

Even product cases:
36 − 9 = 27

Probability (even product) = 27 / 36
= 3/4

Final Answer:
(i) Probability of even sum = 1/2
(ii) Probability of even product = 3/4