Question

Let A and B be two events with P(A) = 0.71 and P(B) = 0.44. What...

Let A and B be two events with P(A) = 0.71 and P(B) = 0.44.

What is the largest possible value of P(A and B)?

What is the smallest possible value of P(A and B)?

Homework Answers

Answer #1

We know that P(A or B) = P(A) + P(B) - P(A and B)

(a) To get the largest possible value of P(A and B), we will have to keep P(A or B) at the least.

We know that P(A and B) is always smaller than or equal to either P(A) or P(B) its Maximum possible value is Minimum [ P(A), P(B)] = MIN[ 0.71, 0.44].

Therefore Maximum of P(A and B) = 0.44

___________________________________________________

If we want the maximum value of P(A or B) which can be 1, then P(A and B) has to be the minimum possible and ensure that P(A) + P(B) dont cross 1.

We see that P(A) + P(B) = 0.71 + 0.44 = 1.15 which exceeds 1 by 0.15.

Therefore Minimum Value of P(A and B) = 0.15

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given two events A and B such that P(A) =0.2, P(B)=0.3, P(A⋃B) = 0.44. Are A...
Given two events A and B such that P(A) =0.2, P(B)=0.3, P(A⋃B) = 0.44. Are A and B disjoint? Are they independent? Why? Find P(A|B).
Given two events X,Y with P(X)= 4/8 and P(Y)=2/4 1.What is the smallest possible value of...
Given two events X,Y with P(X)= 4/8 and P(Y)=2/4 1.What is the smallest possible value of P (X ∩ Y)? 2 What is the largest possible value, that is, find x and y such that, x≤ P( X ∩ Y ) ≤ y, holds and any value in the closed interval [x,y] is possible
Let A and B be two events such that P(A) = 0.8, P(B) = 0.6 and...
Let A and B be two events such that P(A) = 0.8, P(B) = 0.6 and P(A  B) = 0.4. Which statement is correct? a. None of these statements are correct. b. Events A and B are independent. c. Events A and B are mutually exclusive (disjoint). d. Events A and B are both mutually exclusive and independent. e. Events A and B are the entire sample space.
Let A and B be two independent events such that P(A) = 0.17 and P(B) =...
Let A and B be two independent events such that P(A) = 0.17 and P(B) = 0.63. What is P(A or B)? Your answer should be given to 4 decimal places. An urn contains 27 red marbles, 20 blue marbles, and 42 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red or a blue marble? Your answer should be rounded to 4 decimal places.
True or False: (a) Consider two events A and B such that P r ( A...
True or False: (a) Consider two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∪ B ) = P r ( A ) + P r ( B ) . (b) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A...
Let A and B be two events in a sample space for which P{A}=0.59,P{B}=0.25 P{A}=0.59,P{B}=0.25 and...
Let A and B be two events in a sample space for which P{A}=0.59,P{B}=0.25 P{A}=0.59,P{B}=0.25 and P{A∩B}=0.09 P{A∩B}=0.09 . What is the probability A or B occurs, but not both? Round your answer to 4 decimal places.
Consider two events, A and B, of a sample space such that P(A) = P(B) =...
Consider two events, A and B, of a sample space such that P(A) = P(B) = 0.7 a).Is it possible that the events A and B are mutually exclusive? Explain. b).If the events A and B are independent, find the probability that the two events occur together. c).If A and B are independent, find the probability that at least one of the two events will occur. d).Suppose P(B|A) = 0.5, in this case are A and B independent or dependent?...
Let A and B be events with P(A) = .4, P(B) = .4 , and P(A...
Let A and B be events with P(A) = .4, P(B) = .4 , and P(A U B) = .7 . Are A and B independent? Why?
Let A and B be two events from the sample space S. Given P(A)=0.3, P(B)=0.4 and...
Let A and B be two events from the sample space S. Given P(A)=0.3, P(B)=0.4 and P(A or B)=0.6 Find: a) P(A and B) b) P(not A) c) P(not B) d) P(not(A and B)) e) P(not(A or B))
Let z denote a standard normal random variable. a. Find P(z > 1.48). b. Find P(-0.44...
Let z denote a standard normal random variable. a. Find P(z > 1.48). b. Find P(-0.44 < z < 2.68). c. Determine the value of which satisfies P(z > z. ) = 0.7995. d. Find P(z < –0.87).