Question

Two dice are thrown simultaneously. The probability of getting two numbers whose product is even, is

• A.
  $\frac{2}{3}$
• B.
  $\frac{3}{4}$
• C.
  $\frac{1}{2}$
• D.
  $\frac{7}{15}$

Answer 1

The correct option is B

$\frac{3}{4}$
When two dice are thrown simultaneously, the total number of possible outcomes is $6^2=36.$
The outcomes are shown below:
(2,1), (1,2), (4,1), (3,2), (2,3), (1,4), (6,1), (5,2), (4,3), (3,4), (2,5),(1,6), (6,3), (5,4), (4,5) (3,6) (6,5) (5,6) and (6,6)

Thus, the total number of outcomes whose product is even is 27.

$\therefore$ Probability of getting two numbers whose product is even

$=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{27}{36}=\frac{3}{4}$

Hence, the correct answer is option b.