Question

If two dice are thrown simultaneously, then the probability that the product of the outcomes on both the dice is a multiple of 3 is

• A. $\frac{1}{3}$
• B. $\frac{5}{9}$
• C. $\frac{4}{9}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{5}{9}$

Total number of outcomes when two dice are thrown = 36
Outcomes having product on both dice as a multiple of 3:
(1, 3), (1, 6), (2, 3), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 6), (5, 3), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
$\therefore \text{Total number of favourable outcomes}=20$
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{20}{36}$
$=\frac{5}{9}$
Hence, the correct answer is option (b).