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Chapter 5: Problem 30

Roll a fair six-sided die. a. What is the probability that the die shows an even number or a number less than 4 on top? b. What is the probability the die shows an odd number or a number greater than 4 on top?

Short Answer

Expert verified
a. The probability that the die shows an even number or a number less than 4 is \(\frac{5}{6}\) b. The probability the die shows an odd number or a number greater than 4 is \(\frac{2}{3}\)

Step by step solution

01

Find Even Numbers or Less than Four

First, list the possible outcomes when a die is rolled as {1,2,3,4,5,6}. Now, pick all even numbers from the list that are {2,4,6}, and numbers less than 4 are {1,2,3}. The union of these two outcomes results in {1,2,3,4,6}. There are 5 favorable outcomes.
02

Calculate Probability of Event a

The probability of an event is calculated by dividing the number of favorable outcomes by total possible outcomes. There are 6 total possible outcomes and 5 favorable ones. So, the probability for part a is \(\frac{5}{6}\).
03

Find Odd Numbers or More than Four

Now list all odd numbers from the list which are {1,3,5} and numbers greater than 4 are {5,6}. The union of these two outcomes gives {1,3,5,6}. There are 4 favorable outcomes.
04

Calculate Probability of Event b

Again, there are 6 total possible outcomes and 4 favorable ones. So, the probability for part b is \(\frac{4}{6}\), which simplifies to \(\frac{2}{3}\)

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Most popular questions from this chapter

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