1. Let A and B be events with P(A) = 3/10, P(B) = 4/10), and P(AUB) = 6/10.(a) Compute P(AC).(b) Compute P(AB).(c) Compute P(AC U BC).

From the provided information, P(A) = 3/10, P(B) = 4/10, and P(A U B) = 6/10

Answered: Let A and B be events with P(A) = 3/10,…

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

Similar questions

P,Q are independent events
Show that the probability that an event A or an event B or both will occur is given by the formula P(AUB) = P(A)+P(B)– P(AnB), and specialise this formula for the case (a) when A, B are mutually exclusive events and for the case (b) where A, B are statistically independent events. Find the probabilities P(A), P(B) when A, B are statistically independent events such that P(B) = 2P(A) and P(AU B) = 5/8.
) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
Use the attached image to compute the following probabilities:• P(B|A)• P(B ∩ A)• P(B0|A)• P(B0 ∩ A)
(d) P(N and W) P(M and W) (e) P(N or M). Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. No. P(N or M) ≠ 0. No. P(N and M) ≠ 0. Yes. P(N and M) = 0. Yes. P(N or M) = 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. No. P(N and W) = P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W). No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) = P(N) · P(W).
Three events, A, B and C are such that A and B are mutually exclusive, 3 P(4)= P(C|4)= and P(BnC)= 20 (i) Find P(AnC). (ii) Given that P(AnC)=P(BnC)=P(AUBUC), compute P(C). (iii) Hence, calculate P(AUB|C).
For random events A, B, C, prove P(AB) + P(AC) - P(BC) ≤ P(A). Hint: Start with P(AB) = P(ABC) + P(ABC).
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)
3 2 1. Given that P(4)=, P(A/ B)= and P(A/B)=. find : P(ANB) P(B) P(AUB) (а) (i) (ii) (iii) (b) Determine whether the events A and B are : (i) (ii) Mutually exclusive Independent (c) Given that P(A)=0.64 , P(B)=0.36 and P(BnA)= 0.25. Find : (i) P(AOB) (ii) P(AUB) (iii) P(BnA)
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.
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
Show that the probability of the union of events A and B can be written as follows: P(A U B) = P(A) + P(B) [1 - P(A|B) ]

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Let A and B be events with P(A) = 3/10, P(B) = 4/10), and P(AUB) = 6/10. (a) Compute P(AC). (b) Compute P(AB). (c) Compute P(AC U BC).