Question

5. A company sells three models of smartphones: Model A, Model B, and Model C. Of its smartphone sales, 40% are Model A, 30% are Model B, and 30% are Model C. Each model comes with a 2-year warranty. It is known that 15% of Model A smartphones require warranty repair work, while the corresponding percentages for Model B and Model C are 10% and 5%, respectively. (a) What is the probability that a randomly selected purchaser has bought a Model A smart phone that will need repair while under warranty? (b) What is the probability that a randomly selected purchaser has a smartphone that will need repair while under warranty? (c) If a customer returns to the store with a smartphone that needs warranty repair work, what is the probability that it is a Model A? Model B? and Model C?

          5. A company sells three models of smartphones: Model A, Model B, and Model C. Of its smartphone sales, 40% are Model A, 30% are Model B, and 30% are Model C. Each model comes with a 2-year warranty. It is known that 15% of Model A smartphones require warranty repair work, while the corresponding percentages for Model B and Model C are 10% and 5%, respectively.
(a) What is the probability that a randomly selected purchaser has bought a Model A smart phone that will need repair while under warranty?
(b) What is the probability that a randomly selected purchaser has a smartphone that will need repair while under warranty?
(c) If a customer returns to the store with a smartphone that needs warranty repair work, what is the probability that it is a Model A? Model B? and Model C?

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5. A company sells three models of smartphones: Model A, Model B, and Model C. Of its smartphone sales, 40% are Model A, 30% are Model B, and 30% are Model C. Each model comes with a 2-year warranty. It is known that 15% of Model A smartphones require warranty repair work, while the corresponding percentages for Model B and Model C are 10% and 5%, respectively.
(a) What is the probability that a randomly selected purchaser has bought a Model A smart phone that will need repair while under warranty?
(b) What is the probability that a randomly selected purchaser has a smartphone that will need repair while under warranty?
(c) If a customer returns to the store with a smartphone that needs warranty repair work, what is the probability that it is a Model A? Model B? and Model C?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Audrey Fong

02/04/2023

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Step 1: The probability that a randomly selected purchaser has bought a Model A smartphone is 40%. Show more…

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5. A company sells three models of smartphones: Model A, Model B, and Model C. Of its smartphone sales, 40% are Model A, 30% are Model B, and 30% are Model C. Each model comes with a 2-year warranty. It is known that 15% of Model A smartphones require warranty repair work, while the corresponding percentages for Model B and Model C are 10% and 5%, respectively. (a) What is the probability that a randomly selected purchaser has bought a Model A smart phone that will need repair while under warranty? (b) What is the probability that a randomly selected purchaser has a smartphone that will need repair while under warranty? (c) If a customer returns to the store with a smartphone that needs warranty repair work, what is the probability that it is a Model A? Model B? and Model C?

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00:01 In this question, we're given at a store, 20%, 30 % and 50 % of phones are manufactured by factory a, b and c respectively.

00:11 2%, 1 % and 0 .05 % of defective phones are from a, b and c respectively.

00:18 And a customer asks for refund for defective phone.

00:21 I'm going to let a denote the event the phone is from factory a.

00:26 B denote the event, the phones from factory b.

00:29 C denote the event, the phones from factory c.

00:32 And d did not the event, the phone is defective.

00:36 Now let's draw the probability tree.

00:45 Probability the phone is from factory a is 20 % or 0 .2 in decimal.

00:50 Probability the phones from factory b is 0 .3.

00:55 That is 30%.

00:56 And probability the phone is from factory c is 50 % or 0 .5.

01:03 Now they are going to each branch off to event d, which is the phone is defective, or d prime or d complement, the phone is not defective.

01:16 Now over here, this portion here is the phone is defective given that it comes from factory a.

01:23 So that will be 2 % or 0 .02.

01:28 Over here, this is probability the phone is defective given comes from b, and that is 1 % or 0 .01.

01:37 And over here this probability the phone is defective given it comes from c is 0 .05 that will be 0 .005 in decimal.

01:53 In part a we want to find probability the phone is defective.

01:59 So we want to find probability of d.

02:01 That will be taking three mutually exclusive case.

02:05 The first case is a and d.

02:07 Now n is times set notation is intercept or is plus set notation is union...

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