Question

Two dice are thrown. Find the probability of getting an odd number of one die and a multiple of 3 on the other.

Answer 1

Given:

Two fair six-sided dice are thrown once.

Want: one die shows an odd number and the other shows a multiple of 3.

Step-wise calculation:

1. Total possible outcomes = 6 × 6 = 36.

2. Odd faces = {1, 3, 5} (3 choices).

Multiples of 3 = {3, 6} (2 choices).

3. Outcomes with first die odd, second die multiple of 3 = 3 × 2 = 6.

4. Outcomes with first die multiple of 3, second die odd = 2 × 3 = 6.

5. The outcome (3, 3) is counted in both lists, so subtract 1 to avoid double counting.

6. Number of favourable outcomes

= 6 + 6 – 1 

= 11

7. Probability = `"Favourable"/"Total"`

= `11/36`

Required probability = `11/36`.