Answered: Let A and B be events. Point (prove)…

Let A and B be events. Point (prove) that: a. P(A \ B) = P(A) − P(A ∩ B). b) If 0 < P(B) < , and P(A|B) = P(A|Bc), then A⊥B.

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...

See similar textbooks

Related questions

Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…

A: We use the conditional probability formula to prove that A and B are independent.…

Q: Let C and D be events such that Pr[C] =0.8, Pr[D] =0.6,and Pr [C ∪ D] =0.9. Find.. Pr[C |…

A: Given, The objective is to find the required probabilities.

Q: Let A and B be two events with 0 P(B | A). Verify that P(A) > P(B) b.) Suppose that P(A | B) >…

A: a) Given that P(A|B) > P(B|A)or, P(A∩B)P(B)>P(A∩B)P(A)or, 1P(B)>1P(A) [cancel P(A∩B) from…

Q: Supposed P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive. Find: a) P(G)…

A: (a)If events F and G are mutually exclusive, then, P (F or G) = P(F)+ P(G).Or, P(G) = P (F or G) –…

Q: Let us say we have sets/events A, B, and C (do not assume independence). Show that P(A \ B \ C) =…

A: Given: 3 events are given A, B, C Note: I am assuming that in place of (/ or \) their is…

Q: A box contains 40 blocks. For each of the colors red, blue, green, or yellow there are 10 blocks of…

A: Here, given that a box contains 40 blocks. For each of the colors red, blue, green, or yellow there…

Q: Let A, B and D be events. Show that p(A ∪ B|D) = P(A|D) + P(B|D) − ?(A ∩ B|D).

Q: Let A and B be events of positive probability. Prove that P(A|B) ≥ P(A) if and only if P(B|A) ≥…

A: A and B are events of positive probabilityi.e. P(A)>0 and P(B)>0Want to prove that P(A|B) ≥…

Q: True or False: for each of the following statements, decide if it is true or false. If it is rue,…

A: As per given by the question, there are two statement are given and find whether the statement true…

Q: Which of the following statements is true of P(A), that is, the probability of A, for any event A?…

A: Probability defination: Probability may be defined as the ratio of favourable outcome to total…

Q: Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math…

Q: A student stays at home. Let event N = the student watches Netflix. Let event Y = the student…

Q: For any three events A, B, & D. Such that Pr(D)>0. Prove that Pr(A U B|D) = Pr(A|D) ÷ Pr(B|D) - Pr(A…

A: Given that, there are three events A, B & D. We have to prove that, Pr(A U B|D) = Pr(A|D) ÷…

Q: Use Bayes' theorem to solve this problem. A storeowner purchases stereos from two companies. From…

A: 650 stereos are purchased form company A 950 stereos are purchased from company B…

Q: dre ever oddns a. An BCAUB b. Cn (D – E) C ((C n D) – (C n E)) c. FUØ = F

Q: Which of the following are true statements? (Check all that apply) If events A and B are mutually…

A: we have to find true statement for given statements about mutually exclusive and complement events.

Q: 1.) Please find the following probabilities of A, B, C? A.) ?(? ≤ −1.2)= B.) ?(? ≥ 0.08) = C.)…

A: Given: A.) P(Z ≤ −1.2) B.) P(Z ≥ 0.08) C.) P(0.23 ≤ Z ≤ 1.40)

Q: For two events A and B, P(A)=0.24, P(B)=0.57, and P(A∩B)=0.32. a.Find P(A|B) b. Find P(B|A) c.…

Q: Let A and B be events such that Pr[A] =0.370.37, Pr[B] =0.630.63, and Pr[A ∩ B] =0.240.24.…

A: Required to calculate the conditional probability that A occurs given B has occured, P(A|B)

Q: Let A and B be events such that Pr[A] = 0.43, Pr[B] = 0.54, and Pr[A ∩ B] = 0.23. Find …

Question

Let A and B be events. Point (prove) that:

a. P(A \ B) = P(A) − P(A ∩ B).

b) If 0 < P(B) < , and P(A|B) = P(A|Bc), then A⊥B.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

An event F is said to carry negative information about an event F, and we write F E, if P(E|F) < P(E) Prove or give counterexample to the following assertions: If F E, then E F. b. If F NE and E G, then F G а.
T1.2 A person entering a university building is a student (S), faculty (F), or staff (W). We observe three successive persons entering the building. a) List all outcomes in the event A that exactly two are students. b) List all outcomes in the event B that the third person is a faculty
1. a.) What is the probability that A or B occurs? b.) What is the probability that A and B occurs? c.) What is the probability that A or B does not occur?
A student goes to the library. Let event A be that the student checks out a book and event B be that the student uses a library computer. Suppose that we happen to know that P (A) = 0.40, that P (B) = 0.30, and that P (B|A) = 0.5. Compute the following (1) P(Ac)(2) P(A AND B) (3) P(A|B)
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
Let A and B be events such that 0 < P(A) < 1 and 0 < P(B) < 1. a. Show that if A and B are independent, then P(AN B) # 0. b. Show that if P(AN B) = 0, then A and B are not independent
Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).
Determine whether the eventsare independent or dependent. Then find theprobability. A computer program randomly assigns a letter from A to E and a number from 1 to 4 as a user's temporary password. The program assigns C2 as Rebecca's temporary password.
Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math class and a science class while G ∪ H = taking either a math class or a science class. Suppose P(G) = 0.42, P(H) = 0.45, and P(G ∪ H) = 0.25. What is P(G ∩ H)
Show that for any events A and B, P (A ∩ B) ∪ (A ∩ B) = P(A) + P(B) − 2P(A ∩ B)