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(b) P((An B)) Using the Rule for Complements, the probability P((An B)C) can be written as follows. P((An B)C) 1 - P(An B) =P(A)P(B). We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(An B). Note that since we do not know if A and B are independent events, we cannot use the formula P(An To calculate P(An 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.) E₁ E₂ E3 EA Es Step 3 We have found that An B= (E₂). There are five equally likely simple events, E₁, E2, Eg, so each event has probability P(E)= = 0.2. Now calculate the probability P((An B) C). P((An B)C) 1 - P(An B) = 1 - P(E₂) 1-0.2✔ 08 08 0.2)

(b) P((An B)) Using the Rule for Complements, the probability P((An B)C) can be written as follows. P((An B)C) 1 - P(An B) =P(A)P(B). We are given the probabilities P(A) = 0.4 and P(B) = 0.8, but not P(An B). Note that since we do not know if A and B are independent events, we cannot use the formula P(An To calculate P(An 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.) E₁ E₂ E3 EA Es Step 3 We have found that An B= (E₂). There are five equally likely simple events, E₁, E2, Eg, so each event has probability P(E)= = 0.2. Now calculate the probability P((An B) C). P((An B)C) 1 - P(An B) = 1 - P(E₂) 1-0.2✔ 08 08 0.2)

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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Step 4:
Now calculate the probabilities P(AC) and P((A ∩ B)C) by first listing the simple events in AC and (A ∩ B)C. There are five simple events E1, E2, ..., E5. The complement of A is the collection of simple events that are not in A. We are given that A = {E2, E3}, so AC consists of the following event(s). (Select all that apply.)
  • E1
  • E2
  • E3
  • E4
  • E5

We previously found that A ∩ B = {E2}. Therefore, the complement (A ∩ B)C includes the following event(s). (Select all that apply.)

  • E1
  • E2
  • E3
  • E4
  • E5
Tutorial Exercise , E₂1 An experiment can result in one of five equally likely simple events, E₁, A: E₂, E3 P(A) = 0.4 B: E1₁, E₂, E4, E5 P(B) 1' C: E3, E5 P(C) = 0.4 Use the definition of a complementary event to find these probabilities. (a) P(AC) (b) P((An B) C) Step 1 Do the results in part (a) and part (b) agree with the probabilities found by listing the simple events in each event? (a) P(AC) Recall for an event, A, the complement event, AC, is the event that A does not occur. The probability of the complement event is given by the following equation. P(AC) = = 1 - = 1 - P(A) = 0.6 = 0.8 We are given that P(A) = 0.4. Using this value in the above equation, calculate the probability P(AC). P(AC) = 1 - P(A) 0.4 E5. Events A, B, and C are defined as follows. 0.6 0.4
Transcribed Image Text:Tutorial Exercise , E₂1 An experiment can result in one of five equally likely simple events, E₁, A: E₂, E3 P(A) = 0.4 B: E1₁, E₂, E4, E5 P(B) 1' C: E3, E5 P(C) = 0.4 Use the definition of a complementary event to find these probabilities. (a) P(AC) (b) P((An B) C) Step 1 Do the results in part (a) and part (b) agree with the probabilities found by listing the simple events in each event? (a) P(AC) Recall for an event, A, the complement event, AC, is the event that A does not occur. The probability of the complement event is given by the following equation. P(AC) = = 1 - = 1 - P(A) = 0.6 = 0.8 We are given that P(A) = 0.4. Using this value in the above equation, calculate the probability P(AC). P(AC) = 1 - P(A) 0.4 E5. Events A, B, and C are defined as follows. 0.6 0.4
Step 2 (b) P((An B) C) Using the Rule for Complements, the probability P((An 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). {E₂, E3}, and B = To calculate P(A n B), first determine the events in the intersection An B. We are given that A = following event(s). (Select all that apply.) E₁ 0 0 E3 E4 E5 חי Step 3 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 - = 0.8 0.2 0.8 0.2 .../ {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 E5, so each event has probability P(E;) ==== = 0.2. Now calculate the probability P((A n B)C).
Transcribed Image Text:Step 2 (b) P((An B) C) Using the Rule for Complements, the probability P((An 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). {E₂, E3}, and B = To calculate P(A n B), first determine the events in the intersection An B. We are given that A = following event(s). (Select all that apply.) E₁ 0 0 E3 E4 E5 חי Step 3 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 - = 0.8 0.2 0.8 0.2 .../ {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 E5, so each event has probability P(E;) ==== = 0.2. Now calculate the probability P((A n B)C).
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