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(b) P((An B)) Using the Rule for Complements, the probability P((A n B)) can be written a P((An B)C)=1-P(An B) We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(A n B). Note that since we do not know if A and B are independent events, we cannot use the formula P(A n B) = P(A)P(B). To calculate P(A n B), first determine the events in the intersection A n B. We are given that A = {E₂, E3), and B = {E₁, E₂, E4, Es). Their intersection is the collection of simple events that are common to both A and B, so An B includes the following event(s). (Select all that apply.) DE₁ DE₂ follows. DE3 DEA DES

(b) P((An B)) Using the Rule for Complements, the probability P((A n B)) can be written a P((An B)C)=1-P(An B) We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(A n B). Note that since we do not know if A and B are independent events, we cannot use the formula P(A n B) = P(A)P(B). To calculate P(A n B), first determine the events in the intersection A n B. We are given that A = {E₂, E3), and B = {E₁, E₂, E4, Es). Their intersection is the collection of simple events that are common to both A and B, so An B includes the following event(s). (Select all that apply.) DE₁ DE₂ follows. DE3 DEA DES

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(b) P((An B) C) Using the Rule for Complements, the probability P((A n B)) can be written as follows. P((A n B)C) = 1 - P(A n B) We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(A n B). Note that since we do not know if A and B are independent events, we cannot use the formula P(A n B) = P(A)P(B). To calculate P(A n B), first determine the events in the intersection A n B. We are given that A = {E₂, E3}, and B = {E₁, E₂, E4, E5}. Their intersection is the collection of simple events that are common to both A and B, so A n B includes the following event(s). (Select all that apply.) E1 E₂ E3 E4 E5
Transcribed Image Text:(b) P((An B) C) Using the Rule for Complements, the probability P((A n B)) can be written as follows. P((A n B)C) = 1 - P(A n B) We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(A n B). Note that since we do not know if A and B are independent events, we cannot use the formula P(A n B) = P(A)P(B). To calculate P(A n B), first determine the events in the intersection A n B. We are given that A = {E₂, E3}, and B = {E₁, E₂, E4, E5}. Their intersection is the collection of simple events that are common to both A and B, so A n B includes the following event(s). (Select all that apply.) E1 E₂ E3 E4 E5
Expert Solution
Step 1: Determine the given information

The given events are:

A={E2,E3}

B={E1,E2,E4,E5}

The objective is to obtain the intersection of both events, i.e., A∩B.







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We have found that A n B = {E₂}. There are five equally likely simple events, E₁, E₂, P((An B) C) = 1 - P(A n B) = 1 - P(E₂) = 1 - II , E5, so each event has probability P(E;) = 0.2. Now calculate the probability P((A n B)C).
Transcribed Image Text:We have found that A n B = {E₂}. There are five equally likely simple events, E₁, E₂, P((An B) C) = 1 - P(A n B) = 1 - P(E₂) = 1 - II , E5, so each event has probability P(E;) = 0.2. Now calculate the probability P((A n B)C).
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