Question

Gajodhar throws two ordinary dice simultaneously. What is the probability that he shall get two numbers whose product shall be an even number?

• A. $1/3$
• B. $2/3$
• C. $5/16$
• D. $3/8$
• E. $3/4$

Hint:

In probability, it is often much faster to calculate the probability of an event NOT happening and subtracting it from 1. In machine learning, stochastic processes frequently rely on calculating complementary probabilities to optimize decision trees.

Answer 1

Answer: (E)

Step 1: Determine total possible outcomes.
When rolling two dice, the total number of outcomes is $6 \times 6 = 36$.

Step 2: Identify the condition for an even product.
The product of two numbers is even if at least one of the numbers is even. The only way to get an odd product is if BOTH numbers are odd.

Step 3: Calculate the probability using the complement.
The odd numbers on a die are 1, 3, and 5 (3 options).
Number of outcomes where both are odd = $3 \times 3 = 9$.
Outcomes with an even product = $36 - 9 = 27$.
Probability = $\frac{27}{36} = \frac{3}{4}$.