STATISTICS 4.2 HOMEWORK - ADDITION AND MULTIPLICATION RULES
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
