Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

1. $\Big(\dfrac{1}{2}\Big)$

2. $\Big(\dfrac{3}{4}\Big)$

3. $\Big(\dfrac{3}{8}\Big)$

4. $\Big(\dfrac{5}{16}\Big)$

When two dice are thrown simultaneously, each die has 6 possible outcomes.

Total number of outcomes = 36

Let E be the event of getting a product that is even,

The outcomes where both numbers are odd are: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)

Number of outcomes with an odd product = 9

∴ Number of outcomes with an even product = 36 - 9 = 27.

The number of favorable outcomes to the event E = 27

∴ P(E) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{27}{36} = \dfrac{3}{4}$

Hence, option 2 is the correct option.