Given below are two statements in the context of throwing two different dice together:

Statement (I): The probability that the two numbers obtained have an even sum is 0.50.

Statement (II): The probability that the two numbers obtained have an even product is 0.75.

In light of the above statements, choose the most appropriate answer from the options given below.

1. Statement (I): Probability of even sum = $0.50$

Let's verify:

• Possible sums: $2,3,4,5,6,7,8,9,10,11,12$
• Even sums: $2,4,6,8,10,12$
• Let's count favorable outcomes:
  • Sum $2$: $(1,1)$
  • Sum $4$: $(1,3),(2,2),(3,1)$
  • Sum $6$: $(1,5),(2,4),(3,3),(4,2),(5,1)$
  • Sum $8$: $(2,6),(3,5),(4,4),(5,3),(6,2)$
  • Sum $10$: $(4,6),(5,5),(6,4)$
  • Sum $12$: $(6,6)$
• Total favorable outcomes = $18$
• Total possible outcomes = $36$ ($6×6$)
• Probability = $\frac{18}{36} = 0.50$

Therefore Statement (I) is TRUE

2. Statement (II): Probability of even product = $0.75$

Let's verify:

• A product is even if at least one number is even
• On a die, even numbers are $2,4,6$ ($3$ numbers)
• Odd numbers are $1,3,5$ ($3$ numbers)
• For odd product, both numbers must be odd
• Probability of odd product = $\frac{3}{6}×\frac{3}{6} = \frac{1}{4} = 0.25$
• Therefore probability of even product = $1 - 0.25 = 0.75$

Therefore Statement (II) is TRUE

Hence, both statements are true.