Question

odds in favour of getting sum of multiple of 3 when pair of dice is thrown is

• A. 1:2
• B. 1:3
• C. 1:4
• D. 1:5

Answer 1

Answer: (A)

1:2

Answer 2

To find the odds in favor of getting a sum that is a multiple of 3 when a pair of dice is thrown:

1. Total Outcomes: When a pair of dice is thrown, the total number of outcomes is $6 \times 6 = 36$.

2. Favorable Outcomes: We need the sum to be a multiple of 3. The possible sums are 3, 6, 9, and 12.

   • Sum = 3: $(1,2)$ and $(2,1)$ → 2 outcomes.
   • Sum = 6: $(1,5), (2,4), (3,3), (4,2), (5,1)$ → 5 outcomes.
   • Sum = 9: $(3,6), (4,5), (5,4), (6,3)$ → 4 outcomes.
   • Sum = 12: $(6,6)$ → 1 outcome.

   Total Favorable Outcomes = $2 + 5 + 4 + 1 = 12$.

3. Odds in Favour: Odds in favour = (Number of favorable outcomes) : (Number of unfavorable outcomes)

   Here, unfavorable outcomes = $36 - 12 = 24$.

   So, odds in favour = $12:24 = 1:2$.