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(a) Consider three classes, each consisting of 20 students. From this group of 60 students, a group of 3 students is to be chosen. i. What is the probability that all 3 students are in the same class? ii. What is the probability that 2 of the 3 students are in the same class and the other student is in a different class?

(a) Consider three classes, each consisting of 20 students. From this group of 60 students, a group of 3 students is to be chosen. i. What is the probability that all 3 students are in the same class? ii. What is the probability that 2 of the 3 students are in the same class and the other student is in a different class?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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(d) A smartphone company receives shipments of smartphones from three factories, labelled, 1, 2 and 3. Twenty-five percent of shipments come from factory 1 whose shipments contain 8% defective smartphones. Sixty-five percent of the shipments come from factory 2 whose shipments contain 6% defective smartphones. The remainder of the shipments defective comes from factory 3 whose shipments contain 4% smartphones. The company receives a shipment, but does not know the source. A random sample of 15 smartphones is inspected, and three of the smartphones are found to be defective. What is the probability that this shipment came from factory 2?
Transcribed Image Text:(d) A smartphone company receives shipments of smartphones from three factories, labelled, 1, 2 and 3. Twenty-five percent of shipments come from factory 1 whose shipments contain 8% defective smartphones. Sixty-five percent of the shipments come from factory 2 whose shipments contain 6% defective smartphones. The remainder of the shipments defective comes from factory 3 whose shipments contain 4% smartphones. The company receives a shipment, but does not know the source. A random sample of 15 smartphones is inspected, and three of the smartphones are found to be defective. What is the probability that this shipment came from factory 2?
2. (a) Consider three classes, each consisting of 20 students. From this group of 60 students, a group of 3 students is to be chosen. i. What is the probability that all 3 students are in the same class? ii. What is the probability that 2 of the 3 students are in the same class and the other student is in a different class? (b) In a new casino game, two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls to see if you will win any money. Suppose that you win $2 for each black ball selected, you lose $1 for each white ball selected, and you get nothing for each orange ball selected. If the casino lets you play this new casino game with no entry fee, what is the probability that you will not lose any money? (c) A survey was conducted on lawyers at two different law firms about their annual incomes. The following table displays data for the 275 lawyers who responded to the survey. Annual Income Law Firm 1 Law Firm 2 Total Under $45,000 30 20 50 $45,000 to $89,999 35 40 75 $90,000 and over 100 50 150 ТОTAL 165 110 275 2 Suppose we choose a random lawyer who responded to the survey. Are the events "income is under $45,000" and "employed at Law Firm 2" independent?
Transcribed Image Text:2. (a) Consider three classes, each consisting of 20 students. From this group of 60 students, a group of 3 students is to be chosen. i. What is the probability that all 3 students are in the same class? ii. What is the probability that 2 of the 3 students are in the same class and the other student is in a different class? (b) In a new casino game, two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls to see if you will win any money. Suppose that you win $2 for each black ball selected, you lose $1 for each white ball selected, and you get nothing for each orange ball selected. If the casino lets you play this new casino game with no entry fee, what is the probability that you will not lose any money? (c) A survey was conducted on lawyers at two different law firms about their annual incomes. The following table displays data for the 275 lawyers who responded to the survey. Annual Income Law Firm 1 Law Firm 2 Total Under $45,000 30 20 50 $45,000 to $89,999 35 40 75 $90,000 and over 100 50 150 ТОTAL 165 110 275 2 Suppose we choose a random lawyer who responded to the survey. Are the events "income is under $45,000" and "employed at Law Firm 2" independent?
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