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Chapter 11: Problem 11

In Exercises 11-14, a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.

Short Answer

Expert verified
So, the probability of rolling a 2 the first time and a 3 the second time is \(\frac{1}{36}\).

Step by step solution

01

Calculate the probability of the first event

First, determine the likelihood of rolling a 2 on the first try. Since the die has 6 sides and only one side has a 2 on it, the probability P(2 on first roll) of rolling a 2 is given by \(\frac{1}{6}\).
02

Determine the probability of the second event

The second roll is also independent, and thus has the same chance as the first roll for any particular outcome. Hence, the probability P(3 on second roll) of rolling a 3 on the second try is also \(\frac{1}{6}\).
03

Apply the rule of product for independent events

The combined probability of two independent events occurring can be found by multiplying the probabilities of each individual event. Therefore, the probability P( first roll is a 2 and second roll is a 3) = P(2 on first roll) * P(3 on second roll) = \(\frac{1}{6} * \frac{1}{6} = \frac{1}{36}\).

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