A child rolls a standard six-sided die twice. What is the probability of rolling an even number the first time and an even number the second time?

Rationale

The probability of rolling an even number the first time and an even number the second time is {1/4}.

Each roll of a standard six-sided die has three even numbers (2, 4, and 6) out of a total of six possible outcomes. Therefore, the probability of rolling an even number on a single roll is 3/6, which simplifies to 1/2. When rolling the die twice, the probabilities multiply, resulting in (1/2) * (1/2) = 1/4 for both rolls being even.

A (1) YOUR ANSWER

A probability of 1 indicates certainty that an event will occur. In this case, rolling two even numbers is not guaranteed, as there are odd numbers that can be rolled as well. Therefore, the probability cannot be 1.

B ({1/6}) YOUR ANSWER

A probability of {1/6} suggests that there is only one favorable outcome out of six total outcomes. However, since there are three even numbers on the die, this option does not accurately represent the likelihood of rolling an even number.

C ({1/4}) CORRECT

This is the correct answer, as calculated. The probability of rolling an even number on the first roll is 1/2, and the same applies to the second roll. Hence, the combined probability of both rolls resulting in even numbers is (1/2) * (1/2) = 1/4.

D ({1/2}) YOUR ANSWER

A probability of {1/2} indicates that there is a 50% chance of rolling an even number. This only accounts for one roll, not both. For two rolls, the combined probability must be calculated by multiplying the probabilities of each individual roll.

Conclusion

In summary, the probability of rolling an even number on both rolls of a standard six-sided die is {1/4}. Each roll has a 50% chance of yielding an even number, and when considering two independent rolls, the probabilities are multiplied, leading to the final answer of {1/4}. Thus, understanding basic probability principles is essential in solving such problems accurately.

A child rolls a standard six-sided die twice. What is the probability of rolling an even number the first time and an even number the second time?

The probability of rolling an even number the first time and an even number the second time is {1/4}.

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