29. 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?
Answer: C
The probability of rolling an even number the first time and an even number the second time is 1/4.
When rolling a standard six-sided die, the even numbers are 2, 4, and 6. The probability of rolling an even number on one roll is 3 out of 6, or 1/2. Since the rolls are independent, the combined probability of rolling an even number both times is (1/2) * (1/2) = 1/4.
A) 1
This option is incorrect because the probability of rolling an even number on a die cannot be 1. A probability of 1 would mean that it is certain to happen every time, which is not the case with a six-sided die where there are both even and odd outcomes.
B) {1/6}
This option is also incorrect. The probability of rolling an even number is not 1/6, as there are three even numbers (2, 4, and 6) on a six-sided die. Therefore, the probability of rolling an even number in one roll is actually 1/2, not 1/6.
C) {1/4}
This option is correct. The probability of rolling an even number on the first roll is 1/2, and the probability for the second roll is also 1/2. When multiplied together, the probability of both events occurring is (1/2) * (1/2) = 1/4.
D) {1/2}
This option is incorrect because it represents the probability of rolling an even number on a single roll of the die, not the probability of rolling an even number twice in succession. The combined probability requires multiplying the individual probabilities, resulting in 1/4.
Conclusion
The correct answer is 1/4, as it accurately reflects the probability of rolling an even number on both rolls of the die. Options A, B, and D fail to account for the independence of the rolls and the correct calculation of probabilities, while option C correctly applies the multiplication of probabilities for independent events.