Two fair dices, each numbered 1, 2, ..., 6, are tossed together. Find the probability that they both show even numbers.
Answer Details
When two dice are tossed, there are 6 × 6 = 36 possible outcomes, since each die has 6 possible outcomes.
Out of these 36 possible outcomes, there are 3 even numbers on each die (2, 4, 6), so the probability of rolling an even number on a single die is 3/6 = 1/2.
To find the probability that both dice show even numbers, we need to multiply the probability of rolling an even number on the first die (1/2) by the probability of rolling an even number on the second die (also 1/2), since the two events are independent.
So, the probability that both dice show even numbers is:
1/2 × 1/2 = 1/4
Therefore, the answer is option (B) \(\frac{1}{4}\).