Math 227 - Statistics » Spring 2023 » 06KC Complements, Conditional Probability, and Bayes Theorem

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Question #1
Calculate the probability of not rolling a 2. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.8333
B.   0.9222
C.   0.7666
D.   0.6888
Question #2
Find the probability of not drawing a four of diamonds. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.8981
B.   0.9023
C.   0.9808
D.   0.8777
Question #3
Find the probability of not drawing a spade. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.55
B.   0.25
C.   0.85
D.   0.75
Question #4
Blue Productions supplies Blu-ray discs in lots of 72. Blue Productions know that their Blu-ray discs have a reported defect rate of 0.3%.Find the probability of getting at least one defective disc in a lot of 72? (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.1945
B.   0.1235
C.   0.1535
D.   0.2125
Question #5
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Organize the smoking survey results in a gender versus smoking status table. How many non-smokers participated in the survey?
A.   14
B.   16
C.   22
D.   18
Question #6
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a woman from the survey results. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.72
B.   0.44
C.   0.64
D.   0.88
Question #7
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a non-smoker from the survey results. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.64
B.   0.88
C.   0.72
D.   0.76
Question #8
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a non-smoker who is also a woman from the survey results. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.44
B.   0.58
C.   0.66
D.   0.42
Question #9
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a woman who is also a non-smoker from the survey results. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.44
B.   0.46
C.   0.42
D.   0.38
Question #10
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a non-smoker or a woman from the survey results. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.99
B.   0.88
C.   0.92
D.   0.94
Question #11
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a non-smoker from the survey results given that the subject is a woman. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.6744
B.   0.7498
C.   0.6875
D.   0.5476
Question #12
Football fans were surveyed about their smoking habits. Two of nine men smoke, and eleven of sixteen women do not smoke. Find the probability of selecting a woman from the survey results given that the subject is a non-smoker. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.7111
B.   0.6888
C.   0.6111
D.   0.5999
Question #13
In Akutan, Alaska, men are 77% of the population. It is also known 11.3% of Akutan males smoke cigars while 2.1% of Akutan females smoke cigars. One member of the population is selected at random for a survey involving cell phone carriers. Find the probability that the selected subject is male. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.87
B.   0.68
C.   0.73
D.   0.77
Question #14
In Akutan, Alaska, men are 77% of the population. It is also known 11.3% of Akutan males smoke cigars while 2.1% of Akutan females smoke cigars. One member of the population is selected at random for a survey involving cell phone carriers. Find the probability that the selected subject is not male. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.27
B.   0.21
C.   0.13
D.   0.23
Question #15
In Akutan, Alaska, men are 77% of the population. It is also known 11.3% of Akutan males smoke cigars while 2.1% of Akutan females smoke cigars. One member of the population is selected at random for a survey involving cell phone carriers. Express the cigar smoking data as conditional probabilities. Find the probability that the selected subject does not smoke cigars given that the subject is male. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.877
B.   0.817
C.   0.778
D.   0.887
Question #16
In Akutan, Alaska, men are 77% of the population. It is also known 11.3% of Akutan males smoke cigars while 2.1% of Akutan females smoke cigars. One member of the population is selected at random for a survey involving cell phone carriers. Although the subject’s identity is unknown, the scent of cigar smoke is detected. Find the probability that the selected subject is male. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.8234
B.   0.9474
C.   0.9147
D.   0.9684
Question #17
Airbags are manufactured by Aces (A), Best (B), and Cool (C) at rates of 57%, 26% and 17%, respectively. Airbags occasionally kill (K) passengers when they deploy in accidents. Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively. One airbag is randomly selected for testing. Express the airbag manufacturing data as probabilities. Find the probability that a randomly selected airbag was manufactured by Best. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.23
B.   0.22
C.   0.28
D.   0.26
Question #18
Airbags are manufactured by Aces (A), Best (B), and Cool (C) at rates of 57%, 26% and 17%, respectively. Airbags occasionally kill (K) passengers when they deploy in accidents. Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively. One airbag is randomly selected for testing. Express the airbag fatality data as probabilities. Find the probability that a randomly selected airbag killed the passenger given that it was manufactured by Cool. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.15
B.   0.19
C.   0.17
D.   0.13
Question #19
Airbags are manufactured by Aces (A), Best (B), and Cool (C) at rates of 57%, 26% and 17%, respectively. Airbags occasionally kill (K) passengers when they deploy in accidents. Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively. One airbag is randomly selected for testing. If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.5174
B.   0.5785
C.   0.6233
D.   0.4533

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