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Exam 4: Probability

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Question 21

Multiple Choice

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The library is to be given 5 books as a gift. The books will be selected from a list of 20 titles. If each book selected must have a different title, how many possible selections are there?

A) 3,200,000
B) 100
C) 15,504
D) 1,860,480

E) B) and C)
F) A) and C)

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Question 22

Multiple Choice

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Find the indicated probability. Round to the nearest thousandth. -A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 39 that have no defects. What is the probability that at least one of the calculators is Defective?

A) 0.281
B) 0.719
C) 0.707
D) 0.140

E) B) and C)
F) A) and C)

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Question 23

Multiple Choice

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Find the indicated probability. -The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|ccccc} & \text { Occasional } & \begin{array}{c}\text { Regular } \\\text { smoker }\end{array} & \begin{array}{c}\text { Heavy } \\\text { smoker }\end{array} & \text { smoker } & \text { Total } \\\hline \text { Men } & 380 & 48 & 63 & 42 & 533 \\\text { Women } & 360 & 34 & 90 & 47 & 531 \\\text { Total } & 740 & 82 & 153 & 89 & 1064\end{array}$ If one of the 1064 people is randomly selected, find the probability that the person is a man or a heavy smoker.

When asked about the probability that he would become a sumo wrestler, Sam replied "slim to none." Relate that phrase to a numeric probability and interpret his meaning.

Express the indicated degree of likelihood as a probability value. -"Your mother could not have died two years before you were born."

Refer to the table which summarizes the results of testing for a certain disease. $\begin{array}{l|cc} & \text { Positive Test Result } & \text { Negative Test Result } \\\hline \text { Subject has the disease } & 85 & 7 \\\text { Subject does not have the disease } & 27 & 85\end{array}$ A test subject is randomly selected and tested for the disease. What is the probability the subject does not have the disease given that the test result is positive?

Find the indicated probability. -100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time. 1. Public transportation: 7 full time, 8 part time 2) Bicycle: 4 full time, 5 part time 3) Drive alone: 35 full time, 25 part time 4) Carpool: 8 full time, 8 part time

A study of consumer smoking habits includes 162 people in the 18-22 age bracket (57 of whom smoke) , 127 people in the 23-30 age bracket (37 of whom smoke) , and 85 people in the 31-40 age bracket (20 of whom smoke) . If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.

Find the indicated complement. -The probability that Luis will pass his statistics test is 0.67. Find the probability that he will fail his statistics test.

From the information provided, create the sample space of possible outcomes. -Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten?

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - ${ } _ { 5 } \mathrm { P } _ { 4 }$

Compare probabilities and odds. How can you convert odds to probabilities?

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. -The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|crrr} & &\text { Light } & \text { Heavy } \\& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { Total } \\\hline \text { Men } & 358 & 71 & 69 & 498 \\\text { Women } & 304 & 78 & 76 & 458 \\\text { Total } & 662 & 149 & 145 & 956\end{array}$ If one of the 956 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth.

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of Them are acceptable.

Determine whether the events are disjoint. -Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

Suppose a student is taking a 5-response multiple choice exam; that is, the choices are A, B, C, D, and E, with only one of the responses correct. Describe the complement method for determining the probability of getting at least one of the questions correct on the 15-question exam. Why would the complement method be the method of choice for this problem?

Use Bayes' theorem to find the indicated probability. -Use the results summarized in the table. $\begin{array} { l | c c } & \text { Approve of mayor } & \text { Do not approve of mayor } \\\hline \text { Republican } & 15 & 13 \\\text { Democrat } & 20 & 17 \\\text { Independent } & 12 & 23\end{array}$ One of the 100 test subjects is selected at random. Given that the person selected approves of the mayor, what is the probability that they vote Democrat?

Determine whether the events are disjoint. -Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

Provide a written description of the complement of the given event. -Of the thirteen different women Calvin asks for a date, at least one of them accepts.

Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let $1 =$ HIT and $0 =$ OUT. The output from the simulation was as follows. $\begin{array}{llcc}1&0&0&0&1&0&0&1&0&0&1&1&1&1&0&0&0&0&1&1&1&1&0&0&0&0&0&1&1&0&0&1&1&1&1&0&0&0&0&0&0&1&1&1&1&1\end{array}$ Estimate the probability that he gets a hit.