Two fair dices, each numbered 1, 2, ..., 6, are tossed together. Find the probability that they both show even numbers.
Question 1 Report
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) \(\frac{1}{4}\).
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