A box contains a total of 100 CDs that were manufactured on two machines. Of them, 60 weremanufactured on Machine I. Of the total CDs, 15 are defective. Of the 60 CDs that were man-ufactured on Machine I, 9 are defective. Let D be the event that a randomly selected CD isdefective, and let A be the event that a randomly selected CD was manufactured on MachineI. Are events D and A independent?

Independent Event In probability, two factors have been suggested as independent if the happening of…

Answered: A box contains a total of 100 CDs that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Patrick inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.Patrick doesn't know it, but in the batch he is inspecting now, there are 100 products and 12 are defective. If he samples 4 products from this batch without replacement,what is the probability that... a) All of the products in the sample will be defective? b) None of the products in the sample are defective? c) At least one of the products is defective and the whole batch is sent back? For all of the above, round to four decimal places. (answer a b c)
A standard deck of cards consists of 52 cards of 13 types (2,3,...,10,J,Q,K and ace) and 4 colors (hearts, spades, diamonds and clubs), and each combination of type and color appears exactly once. We simultaneously draw 4 cards in random from a standard deck of 52 cards. What is the probability that we drew exactly 2 aces and exactly 2 hearts?
Recently, Hector ran for president of the local school board. Of those who voted in the election, 80% had a high school diploma, and the other 20% did not. Hector got 65% of the vote of those with high school diplomas, while he got only 25% of the vote of those without high school diplomas. Let D denote the event that a randomly chosen voter (in the school board election) had a high school diploma and D denote the event that a randomly chosen voter did not have a high school diploma. Let H denote the event that a randomly chosen voter voted for Hector and H denote the event that a randomly chosen voter did not vote for Hector. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses. (If necessary, consult a list of formulas.)
Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A₁, A₂, and A3 by A₁ = likes vehicle #1 A₂ A3 = likes vehicle #2 = likes vehicle #3. Suppose that P(A₁) = 0.45, P(A₂) = 0.55, P(A3) = 0.70, P(A₁ U A₂) = 0.80, P(A₂ n A3) = 0.50, and P(A₁ U A₂ U A3) = 0.88. (a) What is the probability that the individual likes both vehicle #1 and vehicle #2? 0.2 (b) Determine P(A₂ | A3). (Round your answer to four decimal places.) P(A₂ | A3) = 0.7143 Interpret P(A₂ | A3). If a person likes vehicle #2, this is the probability he or she will also like vehicle #3. This is the probability a person does not like both vehicle #2 and vehicle #3. If a person likes vehicle #3, this is the probability he or she will also like vehicle #2. This is the probability a person likes both vehicle #2 and vehicle #3. (c) Are A₂ and A3 independent events? Answer in two different ways. (Select all that apply.) # Yes. P(A₂ | A3) + P(A₂). Therefore, A₂ and A3…
One card is selected at randon from an ordinary deck of 52 playing cards. Let A= event a face card is selected, B=event a king is selected, and C= event a heart is selected Q: what is P(A | (not B))
Sadie inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.Sadie doesn't know it, but in the batch she is inspecting now, there are 100 products and 11 are defective. If she samples 4 products from this batch without replacement,what is the probability that... a) All of the products in the sample will be defective? b) None of the products in the sample are defective? c) At least one of the products is defective and the whole batch is sent back? For all of the above, round to four decimal places.
A beach resort has 25 jet skis for guests to rent. Of these, 12 are two-person skis, 14 have turbo packs, and 7 are both for two persons and have turbo packs. Let T be the event that a jet ski, randomly chosen, is a two-person ski, and let P be the event that the ski has a turbo pack. A jet ski is chosen at random for rental. Find the probability of "The jet ski is for two persons but does not have turbo packs."

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