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What is the probability of getting a 5 on each of two successive rolls of a balanced die?

Short Answer

Expert verified
The probability of rolling a 5 on both of two successive rolls of a balanced die is \( \frac{1}{36} \).

Step by step solution

01

Determine the probability of rolling a 5 on one roll

A balanced die has 6 sides, equally likely to be rolled. The probability of rolling a 5 on any single roll is the ratio of the number of successful outcomes (rolling a 5) to the total number of equally likely outcomes (rolling any number from 1 to 6). In this case, there is only 1 successful outcome (rolling a 5) out of 6 equally likely outcomes. Therefore, the probability of rolling a 5 is 1/6.
02

Calculate the probability of rolling a 5 on both the first and second rolls

Since the rolls are independent, we can multiply the probabilities of each event occurring to find the overall probability. Using the probability found in step 1, the probability of getting a 5 on both rolls is: \( \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \) So, the probability of rolling a 5 on both of two successive rolls of a balanced die is 1/36.

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