do D part 2. (a) Consider three classes, each consisting of 20 students. From this group of 60 students, agroup 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 otherstudent is in a different class?(b) In a new casino game, two balls are chosen randomly from an urn containing 8 white, 4black, and 2 orange balls to see if you will win any money. Suppose that you win $2 foreach black ball selected, you lose $1 for each white ball selected, and you get nothing foreach orange ball selected. If the casino lets you play this new casino game with no entryfee, 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 IncomeLaw Firm 1 Law Firm 2 TotalUnder $45,000302050$45,000 to $89,999354075$90,000 and over10050150ТОTAL1651102752Suppose we choose a random lawyer who responded to the survey. Are the events "incomeis under $45,000" and "employed at Law Firm 2" independent? (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 shipmentscontain 8% defective smartphones. Sixty-five percent of the shipments come from factory2 whose shipments contain 6% defective smartphones. The remainder of the shipmentsdefectivecomes from factory 3 whose shipments contain 4% smartphones. The company receivesa shipment, but does not know the source.A random sample of 15 smartphones isinspected, and three of the smartphones are found to be defective. What is the probabilitythat this shipment came from factory 2?

Name: do D part 2. (a) Consider three classes, each consisting of 20 student
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Description: do D part 2. (a) Consider three classes, each consisting of 20 students. From this group of 60 students, agroup 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 t

P(F1) = 0.25 P(D intersection F1) = 0.08 P(F2) = 0.65 P(D intersection F2) = 0.06 P(F3) = 1-…

Math

Probability

) 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?

) 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?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

Topic Video

Question

do D part

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?

(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?

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