132 4. A study was conducted in 1997 to measure the total fat content, calories, and sodium content of vegetable burgers available at supermarkets and commonly used as a meat substitute. Measure- ments on 54 different brands of "veggie burgers," and the results were used to develop the 3-way contingency table below. 130 Calories or More Under 130 Calories 320 g Sodium or More Total Fat Under 320 g Under 320 g 320 g Sodium or More Content Sodium Sodium Under 3 g 3 - 4 g Over 4 g 6. 12 3. 6. Total Fat"} %3D onder 130 Calories"}, B = {«320 g Sodium or More" }, C = {“Over 4 g %3D A vegetable burger is selected randomly from the group. Find the following probabilities: (a) P(A) (b) P(B) (c) P(C) (d) P(An B) (e) P(AN BNC) (f) P(AU B) . A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60 mph. A survey of drivers on this portion of the turnpike revealed the following facts: • 18% of the drivers were female • 89% of the drivers were exceeding the speed limit by at least 5 mph (and subject to being stopped) • Of those speeding, 15% of the drivers were female (a) Using F for female and S for speeding, convert each of the bullets above into probability statements. (b) Find the probability that a driver on this stretch of highway is female and exceeding the speed limit. (c) Given a driver on this stretch of highway is female, what is the probability that the driver is speeding? (d) Given that a driver on this stretch of highway speeding, what is the probability that the driver is male? (e) For this stretch of highway, are being female and exceeding the speed limit independent or dependent events? Explain using probabilities. (f) For this stretch of highway, are being female and exceeding the speed limit mutually exclusive (disjoint) events? Explain using probabilities. 6. Suppose we deal three cards from a regular deck of cards without replacement. What is the probability of successively drawing an Ace, a King, and a Queen?
132 4. A study was conducted in 1997 to measure the total fat content, calories, and sodium content of vegetable burgers available at supermarkets and commonly used as a meat substitute. Measure- ments on 54 different brands of "veggie burgers," and the results were used to develop the 3-way contingency table below. 130 Calories or More Under 130 Calories 320 g Sodium or More Total Fat Under 320 g Under 320 g 320 g Sodium or More Content Sodium Sodium Under 3 g 3 - 4 g Over 4 g 6. 12 3. 6. Total Fat"} %3D onder 130 Calories"}, B = {«320 g Sodium or More" }, C = {“Over 4 g %3D A vegetable burger is selected randomly from the group. Find the following probabilities: (a) P(A) (b) P(B) (c) P(C) (d) P(An B) (e) P(AN BNC) (f) P(AU B) . A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60 mph. A survey of drivers on this portion of the turnpike revealed the following facts: • 18% of the drivers were female • 89% of the drivers were exceeding the speed limit by at least 5 mph (and subject to being stopped) • Of those speeding, 15% of the drivers were female (a) Using F for female and S for speeding, convert each of the bullets above into probability statements. (b) Find the probability that a driver on this stretch of highway is female and exceeding the speed limit. (c) Given a driver on this stretch of highway is female, what is the probability that the driver is speeding? (d) Given that a driver on this stretch of highway speeding, what is the probability that the driver is male? (e) For this stretch of highway, are being female and exceeding the speed limit independent or dependent events? Explain using probabilities. (f) For this stretch of highway, are being female and exceeding the speed limit mutually exclusive (disjoint) events? Explain using probabilities. 6. Suppose we deal three cards from a regular deck of cards without replacement. What is the probability of successively drawing an Ace, a King, and a Queen?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Number 4 Parts A, B, and C
Transcribed Image Text:132
4. A study was conducted in 1997 to measure the total fat content, calories, and sodium content of
vegetable burgers available at supermarkets and commonly used as a meat substitute. Measure-
ments on 54 different brands of "veggie burgers," and the results were used to develop the 3-way
contingency table below.
130 Calories or More
Under 130 Calories
320 g Sodium or
More
Total Fat
Under 320 g
Under 320 g
320 g Sodium or
More
Content
Sodium
Sodium
Under 3 g
3 - 4 g
Over 4 g
6.
12
3.
6.
Total Fat"}
%3D
onder 130 Calories"}, B = {«320 g Sodium or More" }, C = {“Over 4 g
%3D
A vegetable burger is selected randomly from the group. Find the following probabilities:
(a) P(A)
(b) P(B)
(c) P(C)
(d) P(An B)
(e) P(AN BNC)
(f) P(AU B)
. A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60 mph. A
survey of drivers on this portion of the turnpike revealed the following facts:
• 18% of the drivers were female
• 89% of the drivers were exceeding the speed limit by at least 5 mph (and subject to being
stopped)
• Of those speeding, 15% of the drivers were female
(a) Using F for female and S for speeding, convert each of the bullets above into probability
statements.
(b) Find the probability that a driver on this stretch of highway is female and exceeding the
speed limit.
(c) Given a driver on this stretch of highway is female, what is the probability that the driver
is speeding?
(d) Given that a driver on this stretch of highway speeding, what is the probability that the
driver is male?
(e) For this stretch of highway, are being female and exceeding the speed limit independent or
dependent events? Explain using probabilities.
(f) For this stretch of highway, are being female and exceeding the speed limit mutually exclusive
(disjoint) events? Explain using probabilities.
6. Suppose we deal three cards from a regular deck of cards without replacement. What is the
probability of successively drawing an Ace, a King, and a Queen?
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