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QUESTION 5 Three machines M1, M2, and M3 produce 40%, 45%, and 15%, respectively, of the total number of nuts produced by a certain factory. The percentages of defective output of these machines are 3%, 6%, and 9%. A) If a nut is selected at random, find the probability that the item is defective. B) Suppose that a nut is selected at random and is found to be defective. Find the probability that the defective nut was produced by machine M1. Let: M1 = produced by machine 1 M2 = produced by machine 2 M3 = produced by machine 3 D = nut is defective D' = nut is not defective Which of the following is the correct representation of the given probability of 9%? P(D | M3) = 0.09 P(D ∩ M3) = 0.09 P(M3 | D) = 0.09 P(M3 ∩ D) = 0.09 QUESTION 6 The route used by a certain motorist in commuting to work contains two intersections with traffic signal lights. The probability that she must stop at the first signal and second signal are 0.40 and 0.50, respectively. The probability that she must stop at either signal is 0.60. What is the probability that she must stop at the first signal but not the second signal. Let: F = must stop at first signal F' = do not have to stop at first signal S = must stop at second signal S' = do not have to stop at second signal Match the correct probability description to each given probability value. A. P(S) B. P(F ∩ S') C. P(F) D. P(F | S') E. P(S' | F) F. P(F ∩ S) G. P(F ∪ S) QUESTION 7 In a manufacturing process, 10% of the parts contain visible surface flaws and 25% of the parts with surface flaws are (functionally) defective parts. However, only 5% of parts without surface flaws are defective parts. The probability of a defective part depends on our knowledge of the presence or absence of a surface flaw. If a part is selected at random, what is the probability it will have a surface flaw and be defective? Let: F = part has surface flaw F' = part does not have surface flaw D = part is defective D' = part is not defective Which of the following probability statements correctly identifies what this problem is asking you to find? P(D | F) P(F ∩ D) P(F U D) P(F | D) QUESTION 8 The probability that the first stage of a numerically controlled machining operation for high-rpm pistons meets specifications is 0.90. Failures are due to metal variations, fixture alignment, cutting blade condition, vibration, and ambient environmental conditions. Given that the first stage meets specifications, the probability that a second stage of machining meets specifications is 0.95. What is the probability that both stages meet specifications? Let: F = the first stage of machining meets specifications F' = the first stage of machining does not meet specifications S = the second stage of machining meets specifications S' = the second stage of machining does not meet specifications Which of the following statements correctly identifies the given probability of 0.95? P(S ∩ F) P(F | S) P(S) P(S | F) QUESTION 9 A football pundit states that the probability that UNC will beat NC State is 0.4, while the probability that UNC will beat Duke is 0.8. Assuming the events are independent, what is the probability that A) UNC wins both games? B) UNC wins at least one game? C) UNC loses both games? Let: N = UNC beats NC State N' = UNC does not beat NC State D = UNC beats Duke D' = UNC does not beat Duke Match the given probability value or listed probability to find with the correct probability statement. A) UNC wins both games? B) UNC wins at least one game? C) UNC loses both games A. P(D) B. P(N ∩ D) C. P (N | D) D. P(N ∪ D) E. P(N' ∩ D') F. P(N) G. P(N ∪ D)

Name: question 5 three machines m1 m2 and m3 produce 40 45 and 15 respectively of the total number of nuts produced by a certain factory the percentages of defective output of these machines are 3 57779
Uploaded: 2023-02-07T01:37:41-08:00
Duration: 2 min 50 s
Channel: Lucas Finney
Description: question 5 three machines m1 m2 and m3 produce 40 45 and 15 respectively of the total number of nuts produced by a certain factory the percentages of defective output of these machines are 3 57779

          QUESTION 5
Three machines M1, M2, and M3 produce 40%, 45%, and 15%, respectively, of the total number of nuts produced by a certain factory. The percentages of defective output of these machines are 3%, 6%, and 9%. A) If a nut is selected at random, find the probability that the item is defective. B) Suppose that a nut is selected at random and is found to be defective. Find the probability that the defective nut was produced by machine M1.

Let:
M1 = produced by machine 1
M2 = produced by machine 2
M3 = produced by machine 3
D = nut is defective
D' = nut is not defective

Which of the following is the correct representation of the given probability of 9%?
P(D | M3) = 0.09
P(D ∩ M3) = 0.09
P(M3 | D) = 0.09
P(M3 ∩ D) = 0.09

QUESTION 6
The route used by a certain motorist in commuting to work contains two intersections with traffic signal lights. The probability that she must stop at the first signal and second signal are 0.40 and 0.50, respectively. The probability that she must stop at either signal is 0.60. What is the probability that she must stop at the first signal but not the second signal.

Let:
F = must stop at first signal
F' = do not have to stop at first signal
S = must stop at second signal
S' = do not have to stop at second signal

Match the correct probability description to each given probability value.

A. P(S)
B. P(F ∩ S')
C. P(F)
D. P(F | S')
E. P(S' | F)
F. P(F ∩ S)
G. P(F ∪ S)

QUESTION 7
In a manufacturing process, 10% of the parts contain visible surface flaws and 25% of the parts with surface flaws are (functionally) defective parts. However, only 5% of parts without surface flaws are defective parts. The probability of a defective part depends on our knowledge of the presence or absence of a surface flaw. If a part is selected at random, what is the probability it will have a surface flaw and be defective?

Let:
F = part has surface flaw
F' = part does not have surface flaw
D = part is defective
D' = part is not defective

Which of the following probability statements correctly identifies what this problem is asking you to find?
P(D | F)
P(F ∩ D)
P(F U D)
P(F | D)

QUESTION 8
The probability that the first stage of a numerically controlled machining operation for high-rpm pistons meets specifications is 0.90. Failures are due to metal variations, fixture alignment, cutting blade condition, vibration, and ambient environmental conditions. Given that the first stage meets specifications, the probability that a second stage of machining meets specifications is 0.95. What is the probability that both stages meet specifications?

Let:
F = the first stage of machining meets specifications
F' = the first stage of machining does not meet specifications
S = the second stage of machining meets specifications
S' = the second stage of machining does not meet specifications

Which of the following statements correctly identifies the given probability of 0.95?
P(S ∩ F)
P(F | S)
P(S)
P(S | F)

QUESTION 9
A football pundit states that the probability that UNC will beat NC State is 0.4, while the probability that UNC will beat Duke is 0.8. Assuming the events are independent, what is the probability that A) UNC wins both games? B) UNC wins at least one game? C) UNC loses both games?

Let:
N = UNC beats NC State
N' = UNC does not beat NC State
D = UNC beats Duke
D' = UNC does not beat Duke

Match the given probability value or listed probability to find with the correct probability statement.

A) UNC wins both games?
B) UNC wins at least one game?
C) UNC loses both games

A. P(D)
B. P(N ∩ D)
C. P (N | D)
D. P(N ∪ D)
E. P(N' ∩ D')
F. P(N)
G. P(N ∪ D)

Added by Edward B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lucas Finney

02/07/2023

Step 1

Given: - Probability of defective output from machine M1 = 3% = 0.03 - Probability of defective output from machine M2 = 6% = 0.06 - Probability of defective output from machine M3 = 9% = 0.09 - Percentage of total nuts produced by M1 = 40% = 0.4 - Percentage of Show more…

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QUESTION 5 Three machines M1, M2, and M3 produce 40%, 45%, and 15%, respectively, of the total number of nuts produced by a certain factory. The percentages of defective output of these machines are 3%, 6%, and 9%. A) If a nut is selected at random, find the probability that the item is defective. B) Suppose that a nut is selected at random and is found to be defective. Find the probability that the defective nut was produced by machine M1. Let: M1 = produced by machine 1 M2 = produced by machine 2 M3 = produced by machine 3 D = nut is defective D' = nut is not defective Which of the following is the correct representation of the given probability of 9%? P(D | M3) = 0.09 P(D ∩ M3) = 0.09 P(M3 | D) = 0.09 P(M3 ∩ D) = 0.09 QUESTION 6 The route used by a certain motorist in commuting to work contains two intersections with traffic signal lights. The probability that she must stop at the first signal and second signal are 0.40 and 0.50, respectively. The probability that she must stop at either signal is 0.60. What is the probability that she must stop at the first signal but not the second signal. Let: F = must stop at first signal F' = do not have to stop at first signal S = must stop at second signal S' = do not have to stop at second signal Match the correct probability description to each given probability value. A. P(S) B. P(F ∩ S') C. P(F) D. P(F | S') E. P(S' | F) F. P(F ∩ S) G. P(F ∪ S) QUESTION 7 In a manufacturing process, 10% of the parts contain visible surface flaws and 25% of the parts with surface flaws are (functionally) defective parts. However, only 5% of parts without surface flaws are defective parts. The probability of a defective part depends on our knowledge of the presence or absence of a surface flaw. If a part is selected at random, what is the probability it will have a surface flaw and be defective? Let: F = part has surface flaw F' = part does not have surface flaw D = part is defective D' = part is not defective Which of the following probability statements correctly identifies what this problem is asking you to find? P(D | F) P(F ∩ D) P(F U D) P(F | D) QUESTION 8 The probability that the first stage of a numerically controlled machining operation for high-rpm pistons meets specifications is 0.90. Failures are due to metal variations, fixture alignment, cutting blade condition, vibration, and ambient environmental conditions. Given that the first stage meets specifications, the probability that a second stage of machining meets specifications is 0.95. What is the probability that both stages meet specifications? Let: F = the first stage of machining meets specifications F' = the first stage of machining does not meet specifications S = the second stage of machining meets specifications S' = the second stage of machining does not meet specifications Which of the following statements correctly identifies the given probability of 0.95? P(S ∩ F) P(F | S) P(S) P(S | F) QUESTION 9 A football pundit states that the probability that UNC will beat NC State is 0.4, while the probability that UNC will beat Duke is 0.8. Assuming the events are independent, what is the probability that A) UNC wins both games? B) UNC wins at least one game? C) UNC loses both games? Let: N = UNC beats NC State N' = UNC does not beat NC State D = UNC beats Duke D' = UNC does not beat Duke Match the given probability value or listed probability to find with the correct probability statement. A) UNC wins both games? B) UNC wins at least one game? C) UNC loses both games A. P(D) B. P(N ∩ D) C. P (N | D) D. P(N ∪ D) E. P(N' ∩ D') F. P(N) G. P(N ∪ D)