Question
If you roll 2 number cubes, what is the probability that the second cube will land on an even number, given that the first cube also lands on an even number?
Answers
GPT-4o mini
To find the probability that the second cube will land on an even number, given that the first cube has landed on an even number, we can analyze the situation step-by-step.
1. **Identify the possible outcomes:** Each number cube (die) has 6 faces, numbered from 1 to 6.
2. **Determine the even numbers on a die:** The even numbers on a standard die are 2, 4, and 6. This means that there are 3 even numbers.
3. **Condition provided:** We know that the first die has landed on an even number. This condition does not affect the probabilities of the outcomes of the second die because the rolls of the two dice are independent events.
4. **Calculate the probabilities of the second die:** Regardless of the outcome of the first die, the second die still has the same probability distribution. Since there are 3 even numbers on the second die (2, 4, and 6), the probability of the second die landing on an even number is calculated as follows:
\[
P(\text{even on second die}) = \frac{\text{Number of even outcomes}}{\text{Total possible outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Thus, the probability that the second cube will land on an even number, given that the first cube also lands on an even number, is:
\[
\frac{1}{2}
\]
1. **Identify the possible outcomes:** Each number cube (die) has 6 faces, numbered from 1 to 6.
2. **Determine the even numbers on a die:** The even numbers on a standard die are 2, 4, and 6. This means that there are 3 even numbers.
3. **Condition provided:** We know that the first die has landed on an even number. This condition does not affect the probabilities of the outcomes of the second die because the rolls of the two dice are independent events.
4. **Calculate the probabilities of the second die:** Regardless of the outcome of the first die, the second die still has the same probability distribution. Since there are 3 even numbers on the second die (2, 4, and 6), the probability of the second die landing on an even number is calculated as follows:
\[
P(\text{even on second die}) = \frac{\text{Number of even outcomes}}{\text{Total possible outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Thus, the probability that the second cube will land on an even number, given that the first cube also lands on an even number, is:
\[
\frac{1}{2}
\]