Q2. Two events A and B are said to be dependent if and only if:(A) P(A) increases along with P(B)(B) P(A) increases as P(B) decreases(C) event A is affected or changed by the occurrence of event B(D) P(A) = P(B)(E) P(ANB) = 0

Here use basic of dependent events

Answered: Q2. Two events A and B are said to be…

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...

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T1.2 A person entering a university building is a student (S), faculty (F), or staff (W). We observe three successive persons entering the building. a) List all outcomes in the event A that exactly two are students. b) List all outcomes in the event B that the third person is a faculty
Prove the following theorem: If A and B are independent, then so are the following pairs of events: 1. A and Bc 2. AC and B 3. AC and BC
15 IF A and B are independent events, prove that the events Ã and B, Ã and B; and A and B are also independent.
) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
QI. Let E, F, and G be three events. Find expressions for the events so that, of E, F. and G. (a) only E occurs, (b) both E and G, but not F.occur: (c) at least one of the events occurs; (d) at least two of the events occur. (e) all three events occCur; (f) none of the eventS OCcurs: () at most one of the events ocurs; (h) at most two of the events occur, (i) exactly two of the events occur; ) at most three of the events occur.
30% of students take Physics101 and 20% take Math146. Of the students who take Physics 101, 25% also take Math146. The events taking Physics 101 and Math146 are O a. independent O b. dependent O c. Disjoint d. None of the above
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.
Suppose that A and B are independent events such that =PA0.30 and =PB0.40 . Find P∩AB and P∪AB . (If necessary, consult a list of formulas.) (a) =P∩AB (b) =P∪AB
Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).
Determine whether the eventsare independent or dependent. Then find theprobability. A computer program randomly assigns a letter from A to E and a number from 1 to 4 as a user's temporary password. The program assigns C2 as Rebecca's temporary password.
(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
IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also independent.

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