Answered: If P(A) > 0, P(B) > 0, and P(A n B) =…

Math

Probability

If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent. true or false?

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: Two events can be both Dependent and NOT Disjoint. True False

Q: A and B are independent events. If Pr(A∩B)=0.18 and Pr[A]=0.3 what is Pr[B]?

A: Independent events : The event A and event B are independent if , P( A∩B ) = P( A )×P( B )

Q: If A and B are events such that P(A)equals=0.60 and P(A∪B)equals=0.70, find P(B) when (a) A…

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

Q: Marcus has a bag that contains 5 identically shaped boxes. 3 of the boxes are blue, and 2 are green.…

A: A : The box is blue B : The box contains a prize. Given, out of 5 boxes 3 are blue , 2 of the blue…

Q: Assume that A and B are events. If P(A∪B)=0.7, P(A)=0.2, and P(B)=0.65, find P(A∩B).

Q: 4a) It is known that P(AB)-0.45, P(B)-0.90 and the events A and B are independent. Find P(A). 0.405…

A: P(A and b ) = 0.45 P(B) = 0.90 P(A) =? Independent events

Q: how that if A1, A2, and A3 are independent events, then P(A1|A2 and A3)

A: Given that A1, A2, and A3 are independent events.

Q: If P(A)=0.2, P(B)=0.1, and P(A∪B)=0.3, then P(A∩B)= Are events A and B independent? Are A and B…

Q: Leon and Zack are playing a game with dice. Leon rolls the dice first, and Zack rolls second. Are…

A: The objective is to check whether two events are dependent or independent.

Q: If A and B are events with P(A)=0.6, P(A OR B)=0.98, P(A AND B)=0.02, find P(B).

Q: If the probability for one and only one event of A and B to happen is 0.3, P (A) = 0.2 and P (B) =…

A: Given: P(A)=0.2 P(B)=0.3 the probability for one and only one event of A and B to happen is 0.3

Q: events A and B are mutually exclusive, then P(A) + P(B) = 0. True or false?

A: Given that If two event A and B are mutually exclusive.

Q: If P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2, then (a) P(E)= (b) P(F)= (c) P(E∪F)= (d) Are the…

A: Given information: P(E∩F)=0.035, P(E|F)=0.14, and P(F|E)=0.2. (a) PF|E=PE∩FPE 0.2 =0.035PE…

Q: Please state if the answer istrue or false. Thank you Two events, A and B, are independent if P(A…

A: Given statement is, Two events, A and B, are independent if P(A and B) = P(A) × P(B)

Q: let a and b be two events with P(A) = 3/8, P(B) = 3/8, and P(A∩B) = 1/8. the value of P(A U B) is

A: From the provided information, P (A) = 3/8 P (B) = 3/8 P (A ∩ B) = 1/8

Q: Assume that A and B are events. If P(A∪B)=0.6, P(A)=0.5, and P(B)=0.25, find P(A∩B).

A: Given information- We have given that A and B are events. P(A)=0.5, P(B)=0.25, P(A∪B)=0.6 We…

Q: If three events A, B and C are independent then P(ANBNC) = P(A) x P(B) x P(C) O True False

Q: An archery game is played by shooting arrows at a target. Each person can choose to have two or…

Q: Fill in the blank to complete the statement below. If two events E and F are not independent, then P…

A: We have given that, If two events E and F are not independent, then P(E and F) = ?

Q: If A and B are events such that P(A)=0.2 and P(A∪B)=0.4, find P(B) when (a) A and B are…

Q: If P(E∩F)=0.09, P(E|F)=0.45P, and P(F|E)=0.5, then (a) P(E)= (b) P(F)= (c) P(E∪F)= (d) Are the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If two events A and B with P(A) = 0.51, P(B) = 0.28 and P(A or B) = 0.79 then, A and B are

A: GivenP(A)=0.51P(B)=0.28P(A or B)=0.79

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

A: Given that P(G) = 0.34, P(H) = 0.32, and P(G ∪ H) = 0.53 What is P(G|H) ?

Q: A and B are independent events. If Pr(A∩B)=0.4 and Pr[A]=0.5 what is Pr[B]Pr[B]?

A: It is given that, P(A)=0.5, P(A and B)=0.4.

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: 2. Draw one card at random from a standard deck of 52 cards. Assume that the cards are equally…

A: A = {x: x is a jack, queen, or king}B= {x: x is a 9, 10, or jack and x is red} C= {x: x is a club}…

Q: A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will…

A: Given Information: A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of…

Q: Suppose two events E and F are independent. Which of the following is true? (1 answer) A. P(E and…

A: Given that two events E and F are independent.

Q: AA and BB are independent events. If Pr(A∩B)=0.28 and Pr[A]=0.4, what is Pr[B]?

Question

If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent.

true or false?

Video Video

Expert Solution

Step 1

Solution-:

If P(A) >0, P(B)>0 and P(A $\cap$ B)=0, then the events A and B are independent.

We find this statement is True / False

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Two events A and B are said to be mutually exclusive if: A. P(A and B) = 0 B. P(A and B) = 1 C. P(A|B) = 1 D. P(BA) = 1
If event A and event B are mutually exclusive, and P(A) = 0.5 and P(B) = 0.3, find P(A and B).
Two events A and B are said to be independent if P(A|B) = P(B). True False
Suppose two doctors, A and B, test all patients coming into a clinic for syphilis. Let events A+ = {doctor A makes a positive diagnosis} and B+ = {doctor B makes a positive diagnosis}. Doctor A diagnoses 25% of all patients as positive, doctor B diagnoses 40% of all patients as positive, and both doctors diagnose 10% of all patients as positive.2.1 Are the diagnoses of the two doctors independent?2.2 Suppose a patient is referred for further lab tests if either doctor A or B makes a positive diagnosis. What is the probability that a patient will be referred for further lab tests?2.3 For a single patient, what is the probability of getting only one positive diagnosis from the two doctors?--------------------------------------------------------------------------------------------------------Suppose there is another doctor, C, who diagnoses 30% of all patients as positive. C's diagnosis is independent of A's and B's.2.4 Let X be the number of positive diagnoses a patient gets. Find the…
If events A and B are independent, then P(A U B) = 0. True or false?
Which of the following is a false statement? O If two events are dependent, the probability of one event effects the probability of the other If two events are dependent, they cannot occur together. OIf two events are independent, the probability of one event has no effect on the probability of the other. If one event is dependent on another, then the second event depends directly on the outcome of the first event. acer F12 Sa Lk Pause Break PriSc F10 F11 F7 F8 F9 F5 420 & %
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.
For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D
(a) For each one of the statements below say whether the statement is true or false, explaining your answer. i. Let A and B be two events such that P(A) > 0 and P(B) > 0. If it holds that P(A|B) = 0, then P(B|A) = 1. 4 i. For two independent events A and B such that P(A) > 0) and P(B) > 0, then: P(AUB) = P(A) = P(B). iii. For a random variable X, then: Var(X)> Var(X + 2). iv. A random sample of size n is a sequence of n independent and non-identically distributed random variables. v. The standard normal distribution has fatter tails than the Student's t distribution with finite degrees of freedom. istribution with