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Chapter 4: Problem 96

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. The probability that a student graduating from this university has student loans to pay off after graduation and is a male is \(.24 .\) Find the conditional probability that a randomly selected student from this university is a male given that this student has student loans to pay off after graduation.

Short Answer

Expert verified
The conditional probability that a randomly selected student is a male given that this student has student loans, is 0.40, or 40%.

Step by step solution

01

Understand the Given Information

Here, the probability of a student having student loans, P(Student Loans) is given as .60, and the probability of a student being a male and having student loans, P(Male and Student Loans) is given as .24.
02

Use the Formula for Conditional Probability

To find the conditional probability P(Male | Student Loans), apply the formula for conditional probability which is P(Male and Student Loans) / P(Student Loans). So, plug the given values into this formula.
03

Calculation

Using the values provided, P(Male | Student Loans) = P(Male and Student Loans) / P(Student Loans) = .24 / .60 = .40. So, the conditional probability that a randomly selected student is a male given they have student loans is .40, or 40%.

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Most popular questions from this chapter

A restaurant chain is planning to purchase 100 ovens from a manufacturer, provided that these ovens pass a detailed inspection. Because of high inspection costs, 5 ovens are selected at random for inspection. These 100 ovens will be purchased if at most 1 of the 5 selected ovens fails inspection. Suppose that there are 8 defective ovens in this batch of 100 ovens. Find the probability that the batch of ovens is purchased. (Note: In Chapter 5 you will learn another method to solve this problem.)

Find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.18, \quad P(B)=.49\), and \(P(A\) and \(B)=.11\) b. \(P(A)=.73, \quad P(B)=.71\), and \(P(A\) and \(B)=.68\)

The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2001 and 2005, based on gender and whether or not they graduated \(\begin{array}{lcc} \hline & \text { Graduated } & \text { Did Not Graduate } \\ \hline \text { Male } & 126 & 55 \\ \text { Female } & 133 & 32 \\ \hline \end{array}\) a. If one of these players is selected at random, find the following probabilities. i. \(P(\) female and graduated \()\) ii. \(P(\) male and did not graduate \()\) b. Find \(P\) (graduated and did not graduate). Is this probability zero? If yes, why?

Explain the meaning of the union of two events. Give one example.

Given that \(A\) and \(B\) are two mutually exclusive events, find \(P(A\) or \(B\) ) for the following. a. \(P(A)=.47\) and \(P(B)=.32\) b. \(P(A)=.16\) and \(P(B)=.59\)
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