Question

Two dice are thrown simultaneously. The probability of getting a multiple of 3 on one dice and a prime number on the other is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{11}{36}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{11}{36}$

Total number of outcomes when two dice are thrown = 36
Outcomes on a die which are multiple of 3 : 3, 6
Outcomes on a die which are prime number: 2, 3, 5
Outcomes having a multiple of 3 on one die and a prime
number on the other die:
(2, 3), (2, 6), (3, 2), (3, 3), (3, 5), (3, 6), (5, 3), (5, 6), (6, 2), (6, 3), (6, 5)
$\therefore \text{Total number of favourable outcomes}=11$
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{11}{36}$
Hence, the correct answer is option (c).