/*! 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 2 Suppose that \(E\) and \(F\) are... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 2

Suppose that \(E\) and \(F\) are two events and that \(P(E \text { and } F)=0.6\) and \(P(E)=0.8 .\) What is \(P(F | E) ?\)

Short Answer

Expert verified
0.75

Step by step solution

01

- Understand Given Information

Identify the given values: \(P(E \text{ and } F) = 0.6\) and \(P(E) = 0.8\)
02

- Recall the Formula for Conditional Probability

The formula for conditional probability is \(P(F | E) = \frac{P(E \text{ and } F)}{P(E)}\)
03

- Substitute the Given Values into the Formula

Substitute \(P(E \text{ and } F) = 0.6\) and \(P(E) = 0.8\) into the formula: \[P(F | E) = \frac{0.6}{0.8}\]
04

- Calculate the Result

Perform the division to find \(P(F | E)\): \[P(F | E) = 0.75\]

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.

probability
Probability is a measure of the likelihood that a particular event will occur. It ranges from 0 (the event will not occur) to 1 (the event is certain to occur). For example, when tossing a fair coin, the probability of landing on heads is 0.5, since there are two equally likely outcomes.
When we talk about events in probability, we're often interested in events that occur in combination, like getting two heads when tossing two coins. This is known as joint probability and is represented as \( P(A \text{ and } B) \).
For the given exercise, the joint probability is 0.6, which means there's a 60% chance for both events \(E\) and \(F\) to occur together.
conditional probability formula
Conditional probability is the probability of an event occurring given that another event has already occurred. It's denoted as \( P(A | B) \), which means the probability of event \( A \) happening given that event \( B \) has happened.
The formula for conditional probability is: \[ P(F | E) = \frac{P(E \text{ and } F)}{P(E)} \]
This formula helps us to calculate probabilities under specific conditions. In our exercise, we want to find \( P(F | E) \), meaning the probability of event \(F\) occurring given that event \(E\) is true. We use the values \( P(E \text{ and } F) = 0.6 \) and \( P(E) = 0.8 \).
calculating probabilities
To calculate \( P(F | E) \) using the conditional probability formula, follow these steps:
  • First, identify the given values: \( P(E \text{ and } F) = 0.6 \) and \( P(E) = 0.8 \).
  • Next, substitute these values into the formula: \[ P(F | E) = \frac{P(E \text{ and } F)}{P(E)} \]
  • Then, perform the division: \[ \frac{0.6}{0.8} = 0.75 \]

The result tells us that given event \( E\) has occurred, there is a 75% chance that event \( F\) will occur. This calculation is essential in understanding how the occurrence of one event affects the probability of another event.

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

Six Flags over Mid-America in St. Louis has six roller coasters: The Screamin' Eagle, The Boss, River King Mine Train, Batman the Ride, Mr. Freeze, and Ninja. After a long day at the park, Ethan's parents tell him that he can ride two more coasters before leaving (but not the same one twice). Because he likes the rides equally, Ethan decides to randomly select the two coasters by drawing their names from his hat. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size \(n=2\) (b) What is the probability that Ethan will ride Batman and Mr. Freeze? (c) What is the probability that Ethan will ride the Screamin' Eagle? (d) What is the probability that Ethan will ride neither River King Mine Train nor Ninja?

In Problem \(35,\) we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he receives both recessive alleles. This is not always the case. For example, Huntington's disease only requires one dominant gene for an individual to contract the disease. Suppose a husband and wife, who both have a dominant Huntington's disease allele \((S)\) and a normal recessive allele \((s),\) decide to have a child. (a) List the possible genotypes of their offspring. (b) What is the probability that the offspring will not have Huntington's disease? In other words, what is the probability the offspring will have genotype \(s s ?\) Interpret this probability. (c) What is the probability that the offspring will have Huntington's disease?

Clothing Options A man has six shirts and four ties. Assuming that they all match, how many different shirt-and-tie combinations can he wear?

Find the value of each combination. $$_{52} C_{1}$$

The following data represent, in thousands, the type of health insurance coverage of people by age in the year 2002 $$\begin{array}{llllll}\hline & <18 & 18-44 & 45-64 & >64 \\\\\hline \text { Private } & 49,473 & 76,294 & 52,520 & 20,685 \\\\\hline \text { Government } & 19,662 & 11,922 & 9,227 & 32,813 \\\\\hline \text { None } & 8,531 & 25,678 & 9,106 & 258 \\\\\hline\end{array}$$ (a) What is the probability that a randomly selected individual who is less than 18 years old has no health insurance? (b) What is the probability that a randomly selected individual who has no health insurance is less than 18 years old?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

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.