Question: Given events A and B, show that the probability that exactly one of the events occurs equals P(A) + P(B) 2P(AB).

Given events A and B, show that the probability that exactly one of the events occurs equals 

P(A) + P(B) − 2P(AB).

Step by Step Solution

★★★★★

3.35 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let C AB c UA c B We h... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability With Applications Questions!

Q:

Given events A and B, let I A and I B be the corresponding indicator variables. Find a simple expression for the conditional expectation of I A given I B = 1.

Q:

LetA1, A2, andA3 be three arbitrary events. Show that the probability that exactly one of these three events will occur is Pr(A1) + Pr(A2) + Pr(A3) 2 Pr(A1 A2) 2 Pr(A1 A3) 2 Pr(A2 A3) + 3 Pr(A1...

Q:

Let A1, . . . , An be n arbitrary events. Show that the probability that exactly one of these n events will occur is isj 1 Pr(AnA2nA,)

Q:

Math 533. Question 1: A national standard requires that public bridge over 200 feet in length must be inspected and rated every 2 years. The rating scale ranges from 0 (poorest rating to 0 (highest...

Q:

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Q:

I. Realic el siguiente problema: Para los siguientes datos: EX=41 Ex=149 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6 b) Calcule 1) la media o promedio 2) cuartil-1 3) cuartil-2 o mediana 4) cuartil-3 5)...

Q:

26. Evaluate the expression for the given value of the variable. (2 pts.) 3x2 + 36. 42. 10. x=2 y=5 (2 pts.) Problems 20, 42, 50, 66, 68 Combine like terms. (2 pts.) Solve the equation. (2 pts.) x1 5...

Q:

hi, i need solutions for these problems! thank you so much! MAT1856S/ APM466S Mathematical Theory of Finance Final Exam - April 2003 Problem 1. Consider a call option on a stock. The stock value...

Q:

I: Events A and B are independent. The probability of event A occurring is 0.64 The probability of events A and B occurring together is 0.24. What is the probability of event B? Enter a decimal, to...

Q:

solve the following An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y=the number of points...

Q:

Suppose the output of a temperature sensor is 0 volt for the input 0C and +5 volt for the input 300C. Also when this temperature sensor is relocated from 0C to 200C, it takes 6 seconds to reach 173C....

Q:

Two boxes with different masses are tied together on a frictionless ramp surface. What is the tension in each of the cords? 1.0 kg 2.0 kg 5

Q:

Suppose the firm has a value of $ 1 1 0 , 2 2 2 . 2 2 when it is all equity financed. Now assume the firm issues $ 4 6 , 0 0 0 of debt paying interest of 6 % per year and uses the proceeds to retire...

Q:

=+X, including E(X1), can be obtained, so that one can directly compare the accuracy of the approximation. Does the approximation improve as

Q:

A psychology professor is interested in whether implementing weekly quizzes improves student learning. She decides to use the weekly quizzes in one section of her introductory psychology class and...

Q:

What is the difference between a true experimental design and a quasi-experimental design?

Q:

A researcher is attempting to determine the effects of practice and gender on a timed task. Participants in an experiment are given a computerized search task. They search a computer screen of...

Q:

What is the primary difference between the null and the research hypothesis? What is the importance of assuming the null hypothesis is true

Q:

Lipscomb is set to establish a reorder policy for his remote snack bar located on Vacation Island. He sells 10 cases of soda per day and has a lead-time for delivery of one week. Occasionally, bad...

Q:

Your friend Phil, asks you what you think about a new scratch- off lottery game. It costs $10 to play this game, There are two outcomes for the game (win, lose) and the probability that a player wins...