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Chapter 11: Problem 51

A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

Short Answer

Expert verified
The probability of rolling an even number the first time and a number greater than 2 the second time is \( \frac{1}{3} \).

Step by step solution

01

Determine the probabilities for each individual event

A die has 6 faces, numbered 1 to 6. The even numbers on a die are 2,4,6. Thus, the probability to roll an even number, P(E), is \( \frac{3}{6} = \frac{1}{2} \). The numbers greater than 2 on a die are 3,4,5,6. Therefore, the probability to roll a number greater than 2, P(G), is \( \frac{4}{6} = \frac{2}{3} \).
02

Finding the Probability of Both Events Occurring

The two events are independent, thus their combined probability is calculated by multiplying the individual probabilities. Therefore, the probability of both events happening, P(E and G), is \( P(E) \times P(G) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3} \).

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