EBook Problems Prob Rules
From Socr
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{{hidden|Answer|(a)}} | {{hidden|Answer|(a)}} | ||
| + | ===Problem 13=== | ||
| + | In a recent issue of Science magazine, we read about a new computer-based test for ovarian cancer, "clinical proteomics" that exams a blood sample for the presence of certain patterns of proteins. Ovarian cancer, though dangerous, is very rare, affecting only one in 5000 women. The test is highly sensitive, able to correctly detect the present of ovarian cancer in 99.97% of women who have the disease. However, it is unlikely to be used as a screening test for the general public, because the test gives a false positive 5% of the time. Draw a tree diagram and determine the probability that a woman tests positive using this method. | ||
| + | *Choose one answer. | ||
| + | |||
| + | :''(a) 0.0998*0.05 | ||
| + | |||
| + | :''(b) 0.0002*0.9997 + 0.9998*0.05 | ||
| + | |||
| + | :''(c) (0.9998*0.95)/(0.0002*0.0003 +0.998*0.95) | ||
| + | |||
| + | :''(d) (0.0002*0.9997)/(0.0002*0.9997 + 0.9998*0.05) | ||
| + | |||
| + | :''(e) 0.0002*0.9997 | ||
| + | {{hidden|Answer|(b)}} | ||
| + | |||
| + | ===Problem 14=== | ||
| + | A quality control engineer claims that the number of defective chips manufactured during runs of 100 of these products is independent of the number of runs and that the proportion of defects is about 4 per 100. What is the probability that there will be no defects in the next run of 100 chips? | ||
| + | |||
| + | *Choose one answer. | ||
| + | |||
| + | :''(a) 0.009 | ||
| + | |||
| + | :''(b) None of these values | ||
| + | |||
| + | :''(c) 0.051 | ||
| + | |||
| + | :''(d) 0.034 | ||
| + | |||
| + | :''(e) 0.017 | ||
| + | {{hidden|Answer|(e)}} | ||
<hr> | <hr> | ||
* [[EBook | Back to Ebook]] | * [[EBook | Back to Ebook]] | ||
Revision as of 08:50, 8 January 2009
Contents |
EBook Problems Set - Rules for Computing Probabilities
Problem 1
A professor who teaches 500 students in an introductory psychology course reports that 250 of the students have taken at least one introductory statistics course, and the other 250 have not taken any statistics courses. 200 of the students were freshmen, and the other 300 students were not freshmen. Exactly 50 of the students were freshmen who had taken at least one introductory statistics course. If you select one of these psychology students at random, what is the probability that the student is not a freshman and has never taken a statistics course?
- Choose one answer.
- (a) 30%
- (b) 40%
- (c) 50%
- (d) 60%
- (e) 20%
Problem 2
A box contains 30 pens, where 5 are red, 14 are black, and 11 are blue. If you pick three pens from the box at random without replacement, what is the probability that these three pens will all be black?
- Choose one answer.
- (a) 14/30 + 14/30 + 14/30
- (b) 14/30 + 13/29 + 12/28
- (c) 14/30 x 13/29 x 12/28
- (d) 1 - (14/30 x 13/29 x 12/28)
Problem 3
When three fair dice are simultaneously thrown, which of these three results is least likely to be obtained?
- Choose one answer.
- (a) All three results are equally unlikely.
- (b) Two fives and a 3 in any order.
- (c) A 5, a 3 and a 6 in any order.
- (d) Three 5's.
Problem 4
Records show that in an introductory chemistry course in a college, 20% of the students get an A, 30% get a B, 40% get a C, and 10% get a D. If you pick three students at random, what is the probability that all three will get an A?
- Choose one answer.
- (a) 0.8*0.8*0.8
- (b) 0.2*0.2*0.2
- (c) 200*0.2*0.2*0.2
- (d) 0.2*3
Problem 5
A newly born child is equally likely to be a boy or a girl. What is the probability that in a family of three children there are less than 3 boys?
- Choose one answer.
- (a) 0.125
- (b) 0.75
- (c) 0.875
- (d) 0.5
Problem 6
A professor who teaches 300 students in an introductory psychology course reports that 135 of the students have taken exactly one introductory statistics course, 60 have taken two or more introductory statistics courses, and the other 105 have not taken any statistics courses. If you select one of these psychology students at random, what is the probability that the student has taken at least one statistics class?
- Choose one answer.
- (a) 0.20
- (b) 0.45
- (c) 0.65
- (d) 0.35
Problem 7
Two fair coins are flipped. The probability that both are heads is:
- Choose one answer.
- (a) About 33%
- (b) Exactly 25%
- (c) Exactly 12.5%
- (d) Exactly 50%
- (e) Exactly 75%
Problem 8
Two fair coins are flipped. The probability that the second coin is a head, given that the first was a head, is:
- Choose one answer.
- (a) Exactly 50%
- (b) Exactly 25%
- (c) Exactly 75%
- (d) Exactly 12.5%
- (e) About 33%
Problem 9
In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the prize. After each guess, if the prize has been won, a new prize is randomly placed in one of the 5 boxes. If a person makes 4 guesses, what is the probability that the person wins a prize exactly twice?
- Choose one answer.
- (a) (0.2)^2/(0.8)^2
- (b) 2(0.2)^2*(0.8)^2
- (c) 6(0.2)^2*(0.8)^2
- (d) (0.2)^2*(0.8)^2
- (e) 2!/5!
Problem 10
Suppose that you read that 88% of all college students have working cell phones. If you take a random sample of 20 college students, what are the chances that at least 18 of the 20 will have working cell phones?
- Choose one answer.
- (a) 0.88*20
- (b) 20!/(18!*2!) (0.88)^18 (0.12)^2
- (c) 190*(0.88)^18 (0.12)^2 + 20*(0.88)^19(0.12) + (0.88)^20
- (d) 1 - 190*(0.88)^18 (0.12)^2 + 20*(0.88)^19(0.12) + (0.88)^20
- (e) None of these values
Problem 11
Express Checkout Researchers report that a quarter of the customers who shop for groceries between 5 P.M. and 7 P.M. use express checkout for 10 items or less. Consider 5 randomly selected customers, and let x represent those who use express checkout. Determine the probability that exactly 2 of the 5 customers use express checkout?
- Choose one answer.
- (a) (0.25)^2
- (b) 10*(0.25)^2*(0.75)^3
- (c) 10*(0.25)^2(0.75)^3 + 5*(0.25)^3(0.75)^2 + 5*(0.25)^4(0.75) + (0.25)^5
- (d) Cannot be determined without the data.
Problem 12
Imagine that you are taking a multiple-choice test in a language which is completely unfamiliar to you. Suppose the test has five questions with four choices for each answer and only one of the four choices is correct. If you answer each question independently and at random, what is the probability that you will answer all five questions incorrectly?
- Choose one answer.
- (a) 3/4*3/4*3/4*3/4*3/4
- (b) 1- (3/4*3/4*3/4*3/4*3/4)
- (c) 3/4 + 3/4 + 3/4 + 3/4 + 3/4
- (d) 1- (1/4*1/4*1/4*1/4*1/4)
Problem 13
In a recent issue of Science magazine, we read about a new computer-based test for ovarian cancer, "clinical proteomics" that exams a blood sample for the presence of certain patterns of proteins. Ovarian cancer, though dangerous, is very rare, affecting only one in 5000 women. The test is highly sensitive, able to correctly detect the present of ovarian cancer in 99.97% of women who have the disease. However, it is unlikely to be used as a screening test for the general public, because the test gives a false positive 5% of the time. Draw a tree diagram and determine the probability that a woman tests positive using this method.
- Choose one answer.
- (a) 0.0998*0.05
- (b) 0.0002*0.9997 + 0.9998*0.05
- (c) (0.9998*0.95)/(0.0002*0.0003 +0.998*0.95)
- (d) (0.0002*0.9997)/(0.0002*0.9997 + 0.9998*0.05)
- (e) 0.0002*0.9997
Problem 14
A quality control engineer claims that the number of defective chips manufactured during runs of 100 of these products is independent of the number of runs and that the proportion of defects is about 4 per 100. What is the probability that there will be no defects in the next run of 100 chips?
- Choose one answer.
- (a) 0.009
- (b) None of these values
- (c) 0.051
- (d) 0.034
- (e) 0.017
- Back to Ebook
- SOCR Home page: http://www.socr.ucla.edu
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