Bot GPT 4-o mini To find the probability of rolling a 5 on the first roll of a die and a 3 on the second roll, we need to consider the probabilities of each individual event.
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The probability of rolling a 5 on the first roll of a die:
- There is 1 favorable outcome (rolling a 5) out of 6 possible outcomes (1, 2, 3, 4, 5, 6). Thus, the probability is: \[ P(\text{5 on first roll}) = \frac{1}{6} \]
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The probability of rolling a 3 on the second roll of a die:
- Similarly, there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes. Thus, the probability is: \[ P(\text{3 on second roll}) = \frac{1}{6} \]
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Since the rolls are independent (the outcome of one roll does not affect the other), we can multiply the probabilities of the two independent events: \[ P(\text{5 on first roll and 3 on second roll}) = P(\text{5 on first roll}) \times P(\text{3 on second roll}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]
Therefore, the probability of rolling a 5 on the first roll and a 3 on the second roll is: \[ \boxed{\frac{1}{36}} \]
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