1/1 Practice 2 f 140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to LusLumer requirements. (a) How many different samples are possible? (b) How many samples of five contain exactly one nonconforming chip? (c) How many samples of five contain at least one nonconforming chip?
1/1 Practice 2 f 140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to LusLumer requirements. (a) How many different samples are possible? (b) How many samples of five contain exactly one nonconforming chip? (c) How many samples of five contain at least one nonconforming chip?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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![30.09.2021
IE3101 Introduction to Probability
1/1
Practice 2
f140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to
LusLUmer requirements.
(a) How many different samples are possible?
(b) How many samples of five contain exactly one nonconforming chip?
(c) How many samples of five contain at least one nonconforming chip?
1. In a Nicd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation
states and that is usually found in the following states:
Nickel Charge
Proportions Found
0.17
+2
0.35
+3
0.33
0.15
(a) What is the probability that a cell has at least one of the positive nickel-charged options?
(b) What is the probability that a cell is not composed of a positive nickel charge greater than +3?
2.
If A, B, and C are mutually exclusive events with P(A)=0.2, P(B)=0.3, and P(C)=0.4, determine the following
probabilities:
(a) P(A UB UC)
(b) P(A BnC)
(c) P[(AUB) nC]
(d) P(A'nB'nc')
7. In a two-team basketball play-off, the winner is the first team to win m games.
(a) Counting separately the number of play-offs requiring m, m +1,..., and 2m – 1
games, show that the total number of different outcomes (sequences of wins and
losses by one of the teams) is
(2m -
m -
m
+...+
m-
m-1
(b) How many different outcomes are there in a '2 out of 3' play-off, a '3 out of 5'
play-off, and a '4 out of 7' play-off?
(EXTRA EXERCISE) Each of the possible five outcomes of a random experiment is equally likely. The sample space is (a,
b, c, d, e). Let A denote the event (a, b), and let B denote the event {c, d, e). Determine the following:
1.
(a) P(A)
(b) P(B)
(c) P(A')
(d) P(AUB)
(e) P(AB)
All outcomes are equally likely
(a) P(A) = 2/5
(b) P(B) = 3/5
(c) P(A') = 3/5
(d) P(AUB) = 1
(e) P(AB) = P(Ø)= 0
(EXTRA EXERCISE) The sample space of a random experiment is {a, b, c, d, e) with probabilities 0.1, 0.1, 0.2, 0.4,
and 0.2, respectively. Let A denote the event (a, b, c), and let B denote the event {c, d, e). Determine the following:
2.
(a) P(A)
(b) P(A')
(c) P(AUB)
(d) P(AB)
Answers:
(a) P(A) = 0.4
(b) P(A') = 0.6
(c) P(AUB) = 1 (d) P(AB) = 0.2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9d64dee-1486-4aaf-947f-76cd841d55ac%2Fd69dd195-1ccc-49ed-b54a-e21cfaf9a155%2Fisyhz7n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:30.09.2021
IE3101 Introduction to Probability
1/1
Practice 2
f140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to
LusLUmer requirements.
(a) How many different samples are possible?
(b) How many samples of five contain exactly one nonconforming chip?
(c) How many samples of five contain at least one nonconforming chip?
1. In a Nicd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation
states and that is usually found in the following states:
Nickel Charge
Proportions Found
0.17
+2
0.35
+3
0.33
0.15
(a) What is the probability that a cell has at least one of the positive nickel-charged options?
(b) What is the probability that a cell is not composed of a positive nickel charge greater than +3?
2.
If A, B, and C are mutually exclusive events with P(A)=0.2, P(B)=0.3, and P(C)=0.4, determine the following
probabilities:
(a) P(A UB UC)
(b) P(A BnC)
(c) P[(AUB) nC]
(d) P(A'nB'nc')
7. In a two-team basketball play-off, the winner is the first team to win m games.
(a) Counting separately the number of play-offs requiring m, m +1,..., and 2m – 1
games, show that the total number of different outcomes (sequences of wins and
losses by one of the teams) is
(2m -
m -
m
+...+
m-
m-1
(b) How many different outcomes are there in a '2 out of 3' play-off, a '3 out of 5'
play-off, and a '4 out of 7' play-off?
(EXTRA EXERCISE) Each of the possible five outcomes of a random experiment is equally likely. The sample space is (a,
b, c, d, e). Let A denote the event (a, b), and let B denote the event {c, d, e). Determine the following:
1.
(a) P(A)
(b) P(B)
(c) P(A')
(d) P(AUB)
(e) P(AB)
All outcomes are equally likely
(a) P(A) = 2/5
(b) P(B) = 3/5
(c) P(A') = 3/5
(d) P(AUB) = 1
(e) P(AB) = P(Ø)= 0
(EXTRA EXERCISE) The sample space of a random experiment is {a, b, c, d, e) with probabilities 0.1, 0.1, 0.2, 0.4,
and 0.2, respectively. Let A denote the event (a, b, c), and let B denote the event {c, d, e). Determine the following:
2.
(a) P(A)
(b) P(A')
(c) P(AUB)
(d) P(AB)
Answers:
(a) P(A) = 0.4
(b) P(A') = 0.6
(c) P(AUB) = 1 (d) P(AB) = 0.2
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