/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Suppose the probability you will... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 15

Suppose the probability you will get an \(\mathrm{A}\) in this class is .25 and the probability you will get a \(\mathrm{B}\) is \(.50 .\) What is the probability your grade will be above a \(C ?\)

Short Answer

Expert verified
The probability of your grade being above a C is 0.75.

Step by step solution

01

Understand the Problem

In this problem, we need to find the probability that the grade obtained is above a C, given the individual probabilities of obtaining an A or a B. We are given: \( P(A) = 0.25 \) and \( P(B) = 0.50 \). Grades above a C include both A and B.
02

Calculate the Total Probability

To find the probability of obtaining either an A or a B, we need to sum their individual probabilities since these two events are mutually exclusive. This can be expressed as: \[ P(A \text{ or } B) = P(A) + P(B) \].
03

Perform the Addition

Substitute the given probabilities into the formula: \[ P(A \text{ or } B) = 0.25 + 0.50 \].
04

Compute the Final Result

Add the probabilities together: \[ P(A \text{ or } B) = 0.75 \]. This is the probability that your grade will be above a C.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mutually Exclusive Events
In probability, mutually exclusive events are events that cannot happen at the same time. This means if one event occurs, the other cannot. For instance, in the given exercise, achieving a grade of an A or a B are mutually exclusive events. If you get an A, you cannot simultaneously get a B.
Understanding mutually exclusive events is crucial because it affects how probabilities are calculated. With mutually exclusive events, the probability of either event occurring is simply the sum of their individual probabilities.
For example:
  • If the probability of getting an A is 0.25
  • And the probability of getting a B is 0.50
The probability of getting either an A or a B is 0.75. This simplifies the calculation and helps us understand the chance of outcomes without overlap.
Addition Rule
The addition rule is a fundamental concept in probability. It allows us to find the probability that any one of several mutually exclusive events occurs. For mutually exclusive events, like getting either an A or a B in your class, the addition rule formula is:
\[ P(A \text{ or } B) = P(A) + P(B) \]
This formula is straightforward when dealing with mutually exclusive events because there's no overlap between them.In our context, we use the addition rule to calculate how likely it is to get an A or a B. Since these grades don't happen simultaneously, adding their probabilities gives the total chance of improving beyond a C.
Grades Analysis
Analyzing grades in terms of probability can provide valuable insights about potential outcomes. In this exercise, we look at how likely you are to score above a C in a class, given probabilities for specific grades: A and B.
The key steps involve:
  • Understanding the probability of each grade individually.
  • Using these probabilities to analyze overall grade outcomes.
By applying the concept of mutually exclusive events and the addition rule, you can clearly determine that there's a 75% chance of scoring above a C. This analysis can help you focus more effectively on your studies, knowing where potential outcomes lie. Additionally, it offers a strategic approach in academics by estimating future performance scenarios.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In a management trainee program at Claremont Enterprises, 80 percent of the trainees are female and 20 percent male. Ninety percent of the females attended college, and 78 percent of the males attended college. a. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college? b. Are gender and attending college independent? Why? c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities. d. Do the joint probabilities total 1.00 ? Why?

Define each of these items: a. Conditional probability b. Event c. Joint probability

The chair of the board of directors says, "There is a 50 percent chance this company will earn a profit, a 30 percent chance it will break even, and a 20 percent chance it will lose money next quarter." a. Use an addition rule to find the probability the company will not lose money next quarter. b. Use the complement rule to find the probability it will not lose money next quarter.

The first card selected from a standard 52 -card deck is a king. a. If it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. If the king is not replaced, what is the probability that a king will be drawn on the second selection? c. What is the probability that a king will be selected on the first draw from the deck and another king on the second draw (assuming that the first king was not replaced)?

A firm will promote two employees out of a group of six men and three women. a. List the outcomes of this experiment if there is particular concern about gender equity. b. Which concept of probability would you use to estimate these probabilities?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.