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Chapter 11: Problem 87

If a single die is rolled five times, what is the probability it lands on 2 on the first, third, and fourth rolls, but not on either of the other rolls?

Short Answer

Expert verified
The probability that the die will land on 2 on the first, third, and fourth rolls, but not on either of the other rolls is \( \frac{1}{6} \times \frac{5}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} = \frac{125}{7776} \) or approximately 0.01606.

Step by step solution

01

Determine the Probability of Rolling a 2

The die has 6 faces. Therefore, the probability of rolling a 2 is \( \frac{1}{6} \). This will be the probability for the 1st, 3rd, and 4th rolls.
02

Determine the Probability of Not Rolling a 2

To determine the probability of not rolling a 2, find the probability of rolling any other number besides 2. Since there are 5 other faces on the die, the probability is \( \frac{5}{6} \). This will be the probability for the 2nd and 5th rolls.
03

Multiply all probabilities together

Since each roll is an independent event, the final probability can be found by multiplying the probabilities of each individual roll together. This is given by \( \frac{1}{6} \times \frac{5}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \)

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