STATISTICS 4.2 HOMEWORK - ADDITION AND MULTIPLICATION RULES

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Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If three different orders are​ selected, find the probability that they are all from Restaurant D.

160 (D total)/1092 = 0.1465x3= 0.0031

Which word is associated with multiplication when computing​ probabilities?

And

P(A or B) indicates ______.

The probability that in a single​ trial, event A​ occurs, event B​ occurs, or they both​ occur.

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are​ selected, find the probability that they are both accurate.

a. 0.7672 (981 (accurate)/1120(total) x ''. The events ARE independent. b. 0.7671 (981/1120)(981-1/1120-1). The events ARE NOT independent.

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If one order is​ selected, find the probability of getting an order from Restaurant A or an order that is accurate. Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint​ events?

a. 0.916 -- 962(order accurate)+40(A not accurate)/1094 b. The events ARE NOT disjoint because it IS possible to RECEIVE AN ACCURATE ORDER FROM RESTAURANT A.

Use the following results from a test for marijuana​ use, which is provided by a certain drug testing company. Among 140 subjects with positive test​ results, there are 29 false positive results. Among 160 negative​ results, there are 4 false negative results. a. How many subjects were included in the study? b. How many subjects did not use marijuana? c. What is the probability that a randomly selected subject did not use marijuana?

a. 300 b. 185 -- 156+29 c. 0.617 -- 185/300

In a computer instant messaging​ survey, respondents were asked to choose the most fun way to​ flirt, and it found that P(D)=0.580​, where D is directly in person. If someone is randomly​ selected, what does PD represent, and what is its​ value?

a. P (D-) is the probability of randomly selecting someone who does not choose a direct​ in-person encounter as the most fun way to flirt. b. P(D-) = 1-0.580 = 0.42

When a man observed a sobriety checkpoint conducted by a police​ department, he saw 660 drivers were screened and 5 were arrested for driving while intoxicated. Based on those​ results, we can estimate that P(W)=0.00758​, where W denotes the event of screening a driver and getting someone who is intoxicated. What does PW denote, and what is its value?

a. P(W-) denotes the probability of screening a driver and finding that he or she is not intoxicated. b. P(W-) = 0.99242

There are​ 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without​ replacement, are the selections independent or​ dependent? If the selections are​ dependent, can they be treated as independent for the purposes of​ calculations?

a. The selections are​ dependent, because the selection is done without replacement. b. ​Yes, because the sample size is less than​ 5% of the population.

When using the​ _______ always be careful to avoid​ double-counting outcomes.

addition rule

Events that are​ _______ cannot occur at the same time.

disjoint

A research center poll showed that 76​% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this​ belief?

0.24 -- 100-0.76

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If one order is​ selected, find the probability of getting food that is not from Restaurant A.

0.681 -- 353 (A total)/1108(total) = 0.319; 1-0.319

In a study of helicopter usage and patient​ survival, among the 49,988 patients transported by​ helicopter, 211 of them left the treatment center against medical​ advice, and the other 49,777 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without​ replacement, what is the probability that none of them left the treatment center against medical​ advice?

0.844 -- 49777/49988 ; (ans)^40

What does P(B|A) mean?

Probability of B given A

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are​ selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made with replacement. Are the events​ independent? b. Assume that the selections are made without replacement. Are the events​ independent?

a. 0.0206 --- 161(D total)/1021 (total) x 161/1021 The probability of getting two orders from Restaurant D is 0.0213. The events ARE NOT independent because choosing the first order AFFECTS the probability of the choice of the second order. b. 0.0247 -- 161/1021 x 161-1/1021-1; ARE NOT, DOES NOT AFFECT

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 17​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. a. Find the probability that both denerators fail during a power outage. b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the​ hospital? Assume the hospital needs both generators to fail less than​ 1% of the time when needed.

a. 0.0289 b. 0.9711 -- 1-0.0289 c. No, because noth generators fail about 3% of the time they are needed.

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 18.4​% daily failure rate. a. What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam? b. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam? c. What is the probability of not being awakened if the student uses three independent alarm​ clocks? d. Do the second and third alarm clocks result in greatly improved​ reliability?

a. 0.184 -- 18.4/100 b. 0.03386 -- 0/184x0/184 c. 0.00623 d. Yes, because total malfunction would not be​ impossible, but it would be unlikely.

When randomly selecting​ adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B)the same as P(B|M)​?

a. the probability of getting a male, given that someone with blue eyes has been selected. b. No, because P(B|M)represents the probability of getting someone with blue​ eyes, given that a male has been selected.

Selections made with replacement are considered to be​ _______.

independent

Two events A and B are​ _______ if the occurrence of one does not affect the probability of the occurrence of the other.

independent


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