Question

Let A and B be independent events of some sample space. Using the definition of independence...

Let A and B be independent events of some sample space. Using the definition of independence P(AB) = P(A)P(B), prove that the following events are also independent:


(a) A and Bc


(b) Ac and B


(c) Ac and Bc

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let A and B be two independent events in the sample space S. Which of the...
Let A and B be two independent events in the sample space S. Which of the following statements is/are true? Circle all that apply. [3 marks] (a) The events A and Bc are independent. (b) The events Ac and Bc are independent. (c) The events (A \ B) and (Ac \ Bc) are independent. (d) None of the above.
Let A and B represent events such that P(A) = 0.6, P(B) = 0.4, and P(A...
Let A and B represent events such that P(A) = 0.6, P(B) = 0.4, and P(A ∪ B) = 0.76. Compute: (a) P(A ∩ B) (b) P(Ac ∪ B) (c) P(A ∩ Bc ) (d) Are events A and B mutually exclusive? Are they independent? Explain by citing the definitions of mutual exclusivity and independence.
If A and B are independent events , prove that : 1\ A and B are...
If A and B are independent events , prove that : 1\ A and B are independent 2\ Ac and B are independent   4\Ac and Bc are independent
Suppose events A,B,C,D are mutually independent. Show that events AB and CD are independent. Justify each...
Suppose events A,B,C,D are mutually independent. Show that events AB and CD are independent. Justify each step from the definition of mutual independence.
Prove (a). Events A and B are independent if and only if Ac and Bc are...
Prove (a). Events A and B are independent if and only if Ac and Bc are independent. (b). If events A and B both have a positive probability and are disjoint, then they cannot be independent.
The event (A∪ B∪C)∪ (AC∩BC∩CC) is ∅ the entire sample space S at least for some...
The event (A∪ B∪C)∪ (AC∩BC∩CC) is ∅ the entire sample space S at least for some A, B and C, it is neither ∅ nor the entire sample space S Please also explain.
Let A, B and C be events in a sample space, S. Suppose that S =...
Let A, B and C be events in a sample space, S. Suppose that S = A ∪ B ∪ C, and that the following hold: A ∩ C = ∅, B ∩ C = ∅. Let P(A) = 0.3, P(B) = 0.5 and P(C) = 0.5. Find P(A ∩ B).
Let A1, A2, . . . , An be n independent events in a sample space...
Let A1, A2, . . . , An be n independent events in a sample space Ω, with respective probability pi = P (Ai). Give a simple expression for the probability P(A1 ∪A2 ∪...∪An) in terms of p1, p2, ..., pn. Let us now apply your result in a practical setting: a robot undergoes n independent tests, which are such that for each test the probability of failure is p. What is the probability that the robot fails at least...
Problem 1) Let A, B and C be events from a common sample space such that:...
Problem 1) Let A, B and C be events from a common sample space such that: P(A) = 0.7, P(B) = 0.68, P(C) = 0.50, P(A∩B) = 0.42, P(A∩C) = 0.35, P(B∩C) = 0.34 (2 points) (i) Find P((A ∪ B) 0 ). (1 point) (ii) Find P(A|B). (2 points) (iii) Find P(A ∩ B ∩ C). (1 point) (iv) Are the events B and C independent? Justify your answer.
Let S be a sample space with probability P and let A ⊂ S, B ⊂...
Let S be a sample space with probability P and let A ⊂ S, B ⊂ S be independent events. Given P (B) = 0.3 and P (A ∪ B) = 0.65, find P (A).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT