Show that the probability that an event A or an event B or both will occuris given by the formula P(AUB) = P(A)+P(B)– P(AnB), and specialisethis formula for the case (a) when A, B are mutually exclusive events andfor the case (b) where A, B are statistically independent events.Find the probabilities P(A), P(B) when A, B are statistically independentevents such that P(B) = 2P(A) and P(AU B) = 5/8.

Probability of an event A = P(A) Probability of occurring event B = P(B) Probability of occurring A…

Answered: Show that the probability that an event…

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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We are given that P(A | B) = 0.4 and P(A) = 0.3. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are ---Select--- not independent independent events.So, to determine P(A and B), we can apply the general multiplication rule for events. Recall that P(B) = 0.9. P(A and B) = P(B) · P(A | B)
A sample of water has a 10% chance of containing a organic pollutant Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that the next 18 samples (i) exactly 3 contain the pollutant. (ii) at least two samples contain the gollutant.
If A and B are disjoint events such that P(A) = 0.30 and P(B)=0.50 then P(BNA) = %3D
Show that the multiplication law P(AB) = P(A/B) P(B), established for two events, may be generalized to three events as foilows; %3D P(AOBOC) = P(A/BC) P(B/C) P(C)
Based on a survey, assume that 33% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by three consumers not comfortable, as in this calculation: (0.33)(0.33)(0.33)(0.67)(0.67)(0.67) = 0.0108? Choose the correct answer below. A. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones. B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones. O C. There are other arrangements consisting of three consumers who are comfortable and three who are not. The probabilities corresponding to those other…
The probability of an integrated circuit passing a quality test is F. In a batch of 10 integrated circuits find the probabilities thati. 2 will failii. 8 will passiii. at least 2 will failiv. fewer than 2 will fail.
If the events A and B two disjoint even then P(AnB) =0.2 P(AnB) =0.6 II P(AnB) =0.8 .IV P(AnB) =1 %3D
Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have. P(x) ХP(x) 0.15 1 0.25 0.35 4 0.10 0.05 6 (or more) 0.05 (a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.) (b) In words, what does the expected value in this example represent? O the average number of children married adults in the country have the average number of children adults in the country have O the number of children married adults in the country have O the number of children adults in the country have (c) Find the expected value. (Enter your answer to two decimal place.) children (d) Is it more likely that a married adult will have two to three children or four to six children? How do you know? O it is more likely to have two to three children, with p = 0.35 O it is more likely to have four…
Suppose that events E and F are independent with p(E) =0.7 and p(F) = 0.8 what is p( E and F) . ( round answer to two decimal places)
Assume that two events A and B are mutually exclusive. P(A) =.75, P(B) = .25 What is P(AnB)? What is P(A/B)?
True or False

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