Answered: from section 3.2 of your text, about…

from section 3.2 of your text, about events AA and BB in a sample space SS, but assume that [A]=0.25, Pr[B]=0.5, and Pr[A∩B]=0.15. Compute the following conditional probabilities:

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

from section 3.2 of your text, about events AA and BB in a sample space SS, but assume that [A]=0.25, Pr[B]=0.5, and Pr[A∩B]=0.15.

Compute the following conditional probabilities:

(1) Pr[A|B]=

(2) Pr[B|A]=

Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.

Expert Solution

Step 1

Conditional probability is known as the probability of an event occurring given that the other event has already occurred. The formula of conditional probability is,

$P r (A | B) = \frac{P r (A \cap B)}{P r (B)}$

(1)

Substitute the given values in the above-mentioned formula as follows:

$P r (A | B) = \frac{P r (A \cap B)}{P r (B)} = \frac{0.15}{0.5} = 0.3$

(2)

Substitute the given values in the above-mentioned formula as follows:

$P r (B | A) = \frac{P r (A \cap B)}{P r (A)} = \frac{0.15}{0.25} = 0.6$

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