determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.

determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.

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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Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)
A retailer of automobile parts has four employees, K, L, M, and N, who make mistakes in filling an order one time in 100, four times in 100, two times in 100, and six times in 100. Of all the orders filled, K , L, M, and N fill, respectively, 20%, 40%, 30%, and 10%. If a mistake is found in a particular order, what are the probabilities that it was filled by K, L, M, or N?
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 36% of all purchasers request A, 47% request B, 69% request C, 54% request A or B, 75% request A or C, 76% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
Samsung wants to run ads for its new Galaxy Phone. Based on a survey conducted, Samsung assigned probabilities to the following events: individual purchased a Galaxy Phone with a probability of 55%, individual recalls seeing the ad with a probability 70%, and individual did not purchase the Galaxy Phone nor recalls seeing the ad with a probability of 40%. What is the probability that the individual recalls seeing the ad or purchases the Galaxy Phone? a. 60% b. 30% c. None of these d. 65% e. 45%
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