/*! 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 59 Explain how to find or probabili... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 59

Explain how to find or probabilities with mutually exclusive events. Give an example.

Short Answer

Expert verified
The probability of 'or' with mutually exclusive events is simply the sum of the probabilities of each event. If Event A and Event B are mutually exclusive, then the probability that either A or B will occur is found using the formula: \(P(A \cup B) = P(A) + P(B)\). For instance, with a six-sided dice, where A is getting a 2, and B is getting a 5, the probability that either event A or event B would occur is \(1/3\).

Step by step solution

01

Definition of Mutually Exclusive Events

Mutually exclusive events are events that cannot happen at the same time. In other words, if one event happens, the other one cannot. For example, throwing a dice and getting either 2 or 5.
02

Definition of 'Or' in Probabilities

The term 'or' in probability refers to the occurrence of at least one of the events. For instance, when we say Event A or Event B, it means either A or B or both can occur.
03

Finding 'Or' Probabilities with Mutually Exclusive Events

For mutually exclusive events A and B, the probability that either event A or event B will occur is given by the formula: \(P(A \cup B) = P(A) + P(B)\). The symbol '\(\cup\)' denotes the union of two sets, which corresponds to the 'or' in probabilities.
04

Example of Mutually Exclusive Events and 'Or' Probabilities

Let's consider an example with a six-sided dice. Let's Event A be getting a 2, and Event B be getting a 5. These events are mutually exclusive as you can't get both on a single toss of the dice. Suppose you roll the dice one time, the probability of each event is \(1/6\). So, applying the formula, we get \(P(A \cup B) = P(A) + P(B) = 1/6 + 1/6 = 2/6 = 1/3\). Thus, the chance that either a 2 or a 5 will be rolled on a single toss of a die is \(1/3\).

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!

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

You are dealt one card from a 52 -card deck. Find the probability that you are dealt a red 7 or a black 8 .

Write a formula for the general term (the nth term of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7},\) the seventh term of the sequence. $$ 3,12,48,192, \dots $$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1, and common ratio, r. Find \(a_{30}\) when \(a_{1}=8000, r=-\frac{1}{2}.\)

Use the Fundamental Counting Principle to solve Five singers are to perform at a night club. One of the singers insists on being the last performer of the evening. If this singer's request is granted, how many different ways are there to schedule the appearances?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Assuming the next U.S. president will be a Democrat or a Republican, the probability of a Republican president is 0.5.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.