Let A and B be events in sample space having positive probability. (a) If P(A|B) < P(A), show that P(B|A) < P(B). (b) If A ∩ B = ∅, what is P(B|A)? (c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)? (d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

Let A and B be events in sample space having positive probability. (a) If P(A|B) < P(A), show that P(B|A) < P(B). (b) If A ∩ B = ∅, what is P(B|A)? (c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)? (d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

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: (a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A).

A: As per our guidelines, we are allowed to answer first question only. Thanks Given Events A and B…

Q: Which of the following is NOT necessarily true for mutually exclusive events A and B? P(A B)=0…

A: If A and B are mutually exclusive events, then A∩B=∅. Then, we have P(A∩B)=P(AB)=0. 1.)…

Q: Two events A and B are independent if... There are 3 different formulas to test for probability…

A: We have given thatTwo events A and B are independent

Q: Let A, B be events with P(A) = .60, P(B) = .20, and P(A and B) = .10. Find P(A|B)

Q: Assume that events A and B are independent, and C ⊂ A, and C ⊂ B. Moreover, P(A) = 1/2, P(B) = 2/3,…

Q: Suppose A and B are events of a sample space. Assume that P (A) = .45 P(B) = .30 P(A∪B) = .55…

A: Suppose A and B are events of a sample space. Assume that P (A) = .45 P(B) = .30 P(A∪B) = .55…

Q: Let A and B be events where P(A)= .3, P(B)= .8, and P(A or B)= .9. Compute P( A and B).

A: The objective of this question is to find the probability of both events A and B occurring, denoted…

Q: 7. If A and B are independent events, then P(A and B)) equals a. P(A) + P(B|A). b. P(A) ( P(B).…

A: GivenA and B are independent events. Any two events A, B are independent events if occurrence of one…

Q: a) Given events A, B, and C with their respective probabilities, P(A) = 0.30, P(B) = 0.40 and P(C) =…

A: As per bartleby guidelines we can solve only first question and rest can be reposted

Q: 1) Events A and B are mutually exclusive. P(A) = 0.35, P(B) = 0.56. Find a) p(not A) b) p(A and B)…

A: As per Bartley guideline expert have to answer first question only since I had done all for you.

Q: Given that IP(A) = 0.54 and IP(B) = 0.55 and IP(A ∪ B) = 0.77, (a) Find IP(Ac). (b) Find IP(A ∩ B).…

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

Q: Let A and B be events with P(A) = 7/15, P(B) = 10/15, and P((A U BỊ ) = 4/15 ?What is P(A N B)

Q: The two events A and B are such that P(A)=0.6, P(B)=0.2, p(A|B)= 0.1. Calculate the probabilities…

Q: a. P(A’) d. P(A’∩B’) b. P(A∪B) e. P[(A∪B)’] c. P(A’∩B) f. P(A’∪B)

A: Here use venn diagram to answer the question

Q: Consider the following events for a college student selected at random. A = student is femaleB =…

A: Given that, A = student is femaleB = student is majoring in business

Q: Let A and B be events with P(AUB) = 3/4, P(A ́) = 2/3 and P(A ∩ B) = 1/4, find a) P(A) b) P(B) c)…

A: To find a) P(A) b) P(B) c) P(A ∩ B ́)

Q: Events AA and BB are independent if the occurrence of one does not affect the probability of the…

A: Given that "Events AA and BB are independent if the occurrence of one does not affect the…

Q: For 1-3 using a spinner like the one shown, find P(A or B). 1) A= an even number; B = a number <3 2)…

A: As per the guidelines we will help you with 3 sub questions. If you need help with any other sub…

Q: Given two events A and B , state whether each of the following can be possible or not a) P(A) P(A)…

A: The union of two events is the occurrence of either of them or at least one of them. The…

Q: Suppose P(A) = 0.28 and P(B) = 0.48 and A and B are independent. Events A and B are not disjoint.…

A: Answer is mentioned below

Q: If P(A)=0.3 and P(B)=0.6, find each probability a) P(A and B) if A and B are independent events…

Q: If A and 8 are independent events and P(B) = and P(AB) = then P(A) is: P(AB) = P(A) P(B) P(B) = 1 11…

A: Given that A and B are independent events such that P(B)=3/4 P(A∩B)=1/2 We have to find P(A)

Q: Let A and B be events. Show that each of the following is true. (a) 1+ P(An B) ≥ P(A) + P(B) (b) P…

A: We have to prove the given statements for the probability of events A and B.

Q: you are givin the information that P(A) = 30 and P(B) = 0.40. Do you have enough information to…

Q: Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/5, and P(A|B) + P(B|A) = 2/3. What is…

A: It is given that P(A)=1/3, P(B)=1/5 and P(A|B)+P(B|A)=2/3.

Q: a)Suppose events E and F are mutually exclusive with P(E)= 0.15 and P(F)= 0.75. (i) What is the…

A: We have given that P(E)= 0.15 and P(F)= 0.75. IF A and B are mutually exclusive. P ( A U B ) = 0…

Q: 3. Let (N.U.P) be a probability space and the events A. BE U such that the probabilities are given…

Q: Suppose that A and B are events such that P(A) = 1/3, P(B) = 1/2 and P(A ∪ B) = 5/6. Find (a) P(A ∩…

Q: The following two-way table shows the distribution of daily traffic and weather issues in a certain…

A: Given :

Q: Suppose that A and B are events for which P(A) =0.2, P(B)=0.5, and P(A ∩ B)=0.13 P(B|A)=?

Q: Suppose P(A) = .70, P(B) = .18, and events A and B are mutally exclusive. Find: a) P(A and B) b)…

A: The provided information are :P(A) = 0.70, P(B) = 0.18The events A and B are mutually exclusive.

Q: Given P(A) = 0.3, P(b) = 0.5 and P( A and B ) = 0.2. Are the events A,B independent ?…

A: Thank you for posting the question. Since you have asked multiple question(Different questions), we…

Q: Let A and B be events in a sample space with positive probability. Prove that P(B|A) > P(B) if and…

Q: Let A and B be events with P(A) =0.4, P(B) =0.7, and P(B|A) =0.5. Find P (A and B).

A: The question is about prob. of events Introduction : If A and B are two events then the condition…

Q: P(A) = 0.4 and P(B) = 0.5. Complete parts (a) through (d). Suppose that events A and B are disjoint,…

A: According to the given information in this questionThere are more than three subparts according to…

Q: We are given that P(A | B) = 0.4 and P(A) = 0.3. Since P(A | B) ≠ P(A), the occurrence of…

Question

5) Let A and B be events in sample space having positive probability.
(a) If P(A|B) < P(A), show that P(B|A) < P(B).
(b) If A ∩ B = ∅, what is P(B|A)?
(c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)?
(d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

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: Define two events A and B

Step 2: Part a

Step 3: Part b

Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If A and B are events in a sample space S, then P(ACUBC) is equal to P(AnB) +P(A°). P(AnB) +P(A°) P(ANB“)+P(A) P(AnB) +P(A )
Suppose A and B are events such that P(A) = 0.6 P(B)= 0.7 and P(A or B) = 0.8 What’s P(A) with a little c on top equal to ? What’s P(B) with a little c on top equal to? Are A and B mutually exclusive? Why or why not ? Are A and B independent ? Why or why not ?
b) Events A and B are such that P(A) = 3/5, P(B) = 4/15. Find P(A U B) if i) A and B are mutually exclusive events. (3 marks) ii) A and B are independent events. (3 marks)
Use the appropriate formula to answer the question: • Independent Probability: P(A and B) = P(A) x P(B) • Conditional Probability: P(A n B) = P(A) x P(B|A) • Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) True or False: Events A and B are independent? P(A) = 0.60 P(B) = 0.70 P(A and B) = 0.42 True False
Show that the multiplication law P(AnB) = P(A/B) P(B), established for two events, may be generalized to three events as follows; P(AOBOC) =P(A/BC) P(B/C) P(C) %3D
1. Events A and B are mutually exclusive with P(A) = 0.280 and P(A or B) = 0.740 a) P(B)= b) P(Not A)= c) P(A and B)=
7.3 pt2 Q6) Hey! Need help with the following, it states to answer in integers or fraction, thank you!
The Addition Rule for the probability that events A or B or C will occur, P(A or B or C), is given by P(A or B or C)=P(A) + P(B) + P(C) - P(A and B)- P(A and C) - P(B and C) + P(A and B and C) Find P(A or B or C) for the given probabilities. P(A)=0.38, P(B) = 0.29, P(C) = 0.12 P(A and B)=0.12, P(A and C) = 0.04, P(B and C) = 0.06 P(A and B and C) = 0.01 P(A or B or C) =
Let (A,n 2 1) be independent events. Then a)E=1 P(A,) = 0 == P(A i.o.) = 1 b) En=1 P(A,)<=P(A, i.o.) = 0.
b) Show that the multiplication law P(AB) P(A/B) P(B), established for two events, may be generalized to three events as follows; P(AOBOC) P(A/Bnc) P(B/C) P(C)
The Addition Rule for the probability that events A or B or C will occur, P(A or B or C), is given by P(A or B or C)=P(A) + P(B) + P(C) - P(A and B)- P(A and C) - P(B and C) + P(A and B and C) Find P(A or B or C) for the given probabilities. P(A) = 0.32, P(B) = 0.24, P(C) = 0.11 P(A and B) = 0.13, P(A and C) = 0.03, P(B and C) = 0.08 P(A and B and C) = 0.01 P(A or B or C) = montesino P Pearson DELL S Hummert mana SEFERDESSERTS SIEMENS se fa m Next Copyright © 2022 Pearson Education Inc. All rights reserved. | Terms of Use | Privacy Policy | Permissions Contac