Problem 50
Question
A single die is rolled twice. Find the probability of rolling a 5 the first time and a 1 the second time.
Step-by-Step Solution
Verified Answer
The probability of rolling a 5 on the first roll and a 1 on the second roll is 1/36.
1Step 1: Determine the probability of each individual event
The die used is a fair six-sided die. Therefore, the probability of rolling any number (i.e. 1, 2, 3, 4, 5, or 6) is 1/6. So, the probability of rolling a 5 on the first roll is 1/6 and the probability of rolling a 1 on the second roll is also 1/6.
2Step 2: Apply the rule of product for independent events
To find the combined probability of two independent events occurring, we multiply the probabilities of each individual event. Therefore, the probability of rolling a 5 on the first roll and a 1 on the second roll is \( \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} . \)
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