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Chapter 4: Problem 26

A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained?

Short Answer

Expert verified
The probability that a dice roll results in a number less than 5 is \(\frac{2}{3}\). Similarly, the probability of obtaining a number between 3 and 6 (inclusive) is also \(\frac{2}{3}\).

Step by step solution

01

Identify the total number of outcomes.

When a die is rolled, the total number of outcomes is 6 because a die has six faces, each with a distinct number from 1 to 6.
02

Calculate the probability for part a.

The favorable outcomes for part a are getting the numbers 1, 2, 3, and 4, making a total of 4 favorable outcomes. Hence, the probability of getting a number less than 5 is calculated by dividing the number of favorable outcomes by the total number of outcomes, which is \(\frac{4}{6}\) or \(\frac{2}{3}\).
03

Calculate the probability for part b.

The favorable outcomes for part b are getting the numbers 3, 4, 5, and 6, making a total of 4 favorable outcomes. Hence, the probability of getting a number between 3 and 6 is calculated by dividing the number of favorable outcomes by the total number of outcomes, which is \(\frac{4}{6}\) or \(\frac{2}{3}\).

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Most popular questions from this chapter

The probability that a randomly selected college student attended at least one major league baseball game last year is .12. What is the complementary event? What is the probability of this complementary event?

A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. The following table gives the results of the survey. Assume that none of these 250 students is majoring in both areas. $$ \begin{array}{lcc} \hline & \text { Happy } & \text { Unhappy } \\ \hline \text { Psychology } & 80 & 20 \\ \text { Communication } & 115 & 35 \\ \hline \end{array} $$ a. If one student is selected at random from this group, find the probability that this student is i. happy with the choice of major ii. a psychology major iii. a communication major given that the student is happy with the choice of major iv. unhappy with the choice of major given that the student is a psychology major v. a psychology major and is happy with that major vi. a communication major \(o r\) is unhappy with his or her major b. Are the events "psychology major" and "happy with major" independent? Are they mutually exclusive? Explain why or why not.

What is meant by the joint probability of two or more events? Give one example.

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