If you roll a die twice, what is the probability that both rolls will be even nu

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Question: If you roll a die twice, what is the probability that both rolls will be even numbers?

Options:

Correct Answer: 1/4

Solution:

The even numbers on a die are 2, 4, and 6 (3 out of 6). The probability for one roll is 1/2, so for two rolls, it is (1/2) * (1/2) = 1/4.

If you roll a die twice, what is the probability that both rolls will be even numbers?

If you roll a die twice, what is the probability that both rolls will be even numbers?

Step 1: Understand that a die has 6 sides, numbered from 1 to 6.
Step 2: Identify the even numbers on the die. They are 2, 4, and 6.
Step 3: Count the total number of even numbers. There are 3 even numbers (2, 4, 6).
Step 4: Calculate the probability of rolling an even number on one roll. There are 3 even numbers out of 6 total numbers, so the probability is 3/6, which simplifies to 1/2.
Step 5: Since you are rolling the die twice, you need to find the probability of both rolls being even. This means you multiply the probability of the first roll being even by the probability of the second roll being even.
Step 6: Multiply the probabilities: (1/2) * (1/2) = 1/4.
Step 7: Conclude that the probability of rolling even numbers on both rolls is 1/4.

Probability of Independent Events – The question tests the understanding of calculating the probability of independent events occurring, specifically the probability of rolling even numbers on a die.
Basic Probability Calculation – It assesses the ability to calculate the probability of a single event and extend it to multiple events.