Question
What is the probability of getting a 5 and then a 2 with the normal 6 -sided die? (answer in fraction) Type a response
Ask by Ross Cross. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of rolling a 5 and then a 2 is \(\frac{1}{36}\).
Solution
To find the probability of getting a 5 and then a 2 when rolling a normal 6-sided die, we can follow these steps:
1. **Determine the probability of rolling a 5.**
- There is 1 favorable outcome (rolling a 5) out of 6 possible outcomes (1, 2, 3, 4, 5, 6).
- Therefore, the probability \( P(5) \) is:
\[
P(5) = \frac{1}{6}
\]
2. **Determine the probability of rolling a 2.**
- Similarly, there is 1 favorable outcome (rolling a 2) out of 6 possible outcomes.
- Therefore, the probability \( P(2) \) is:
\[
P(2) = \frac{1}{6}
\]
3. **Calculate the combined probability of both events occurring in sequence.**
- Since the rolls are independent, we multiply the probabilities:
\[
P(5 \text{ and then } 2) = P(5) \times P(2) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
Thus, the probability of rolling a 5 and then a 2 with a normal 6-sided die is \(\frac{1}{36}\).
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Simplify this solution Bonus Knowledge
The probability of rolling a 5 on a 6-sided die is 1 out of 6, or \( \frac{1}{6} \). After rolling a 5, the die is rolled again, and the probability of rolling a 2 is also \( \frac{1}{6} \). To find the probability of both events happening in sequence, you multiply the probabilities: \( \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \). So, the probability of getting a 5 followed by a 2 is \( \frac{1}{36} \).
