Review Problems Solutions

# 205 2 05 f a randomly selected microprocessor is from

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Unformatted text preview: (.035) ≈ .0158 (E) a randomly selected microprocessor is defective given that it is from ﬁrm B? Solution: P (def |B ) = P (def ∩B ) P (B ) = .2(.05) .2 = .05 (F) a randomly selected microprocessor is from ﬁrm A given that it is defective? Solution: P (A|def ) = P (A∩def ) P (def ) = .35(.05) .35(.05)+.2(.05)+.45(.035) 5 ≈ .4046 Problem 7 A survey involving 400 likely Democratic voters and 400 likely Republican voters asked the question: Do you support or oppose legislation that would require trigger locks on guns, to prevent misuse by children? The results are displayed in the table below. Answer Support Oppose Don’t Know Democrats, % 85 10 5 Republicans, % 20 65 15 (A) Draw a tree diagram using the given information. Solution: (B) What is the probability that a randomly selected voter is a likely Republican voter? Solution: P (R) = 400 800 = .5 (C) What is the probability that a randomly selected voter answered “support”? Solution: P (S ) = 400 800 (.20) + 400 800 (.85) = 525 (D) What is the probability that a randomly selected voter is a likely Democratic voter and answered “oppose”? Solution: P (D ∩ O) = 400 800 (.10) = .05 (E) If a randomly selected voter is a likely Democratic voter, what is the probability that he/she answered “support”? Solution: P (S |D) = P (S ∩ D ) P (D ) = 400 800 (.85) 400 800 = .85 (F) If a randomly selected voter answered “oppose”, what is the probability that he/she is a likely Republican voter? Solution: P (R|O) = P (R ∩ O ) P (O ) = 400 800 (.65) 400 (.65)+ 400 (.10) 800 800 ≈ .8667 6 Problem 8 A nationwide survey conducted by the National Cancer Society revealed the following information: Of 10,000 people surveyed, 4000 were &quot;heavy coﬀee drinkers&quot; and 151 had cancer of the pancreas. Of those who had cancer of the pancreas, 121 were heavy coﬀee drinkers. Using the data in this survey determine whether the events &quot;being a heavy coﬀee drinker&quot; and &quot;having cancer of the pancreas&quot; are independent events. Explain your answer. Solution: Let H be the event “being a...
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