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    STAT7055 Spring Session 2017 Topic 2 Tutorial Questions

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    Callum Lowe
    This document contains 5 statistics problems related to probability. Problem 1 asks about the probability that a car will idle roughly given that each of its 4 spark plugs has a 90% chance of functioning properly. Problem 2 asks about the effectiveness of an antidepressant drug on men and women. Problem 3 involves probabilities related to recidivism rates under a proposed new criminal law. Problem 4 asks about probabilities related to flipping biased coins. Problem 5 asks about probabilities related to selecting balls from buckets of different weights.

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    STAT7055 Spring Session 2017 Topic 2 Tutorial Questions

    Uploaded by

    Callum Lowe
    123 views2 pages
    This document contains 5 statistics problems related to probability. Problem 1 asks about the probability that a car will idle roughly given that each of its 4 spark plugs has a 90% chance of functioning properly. Problem 2 asks about the effectiveness of an antidepressant drug on men and women. Problem 3 involves probabilities related to recidivism rates under a proposed new criminal law. Problem 4 asks about probabilities related to flipping biased coins. Problem 5 asks about probabilities related to selecting balls from buckets of different weights.

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    This document contains 5 statistics problems related to probability. Problem 1 asks about the probability that a car will idle roughly given that each of its 4 spark plugs has a 90% chance of functioning properly. Problem 2 asks about the effectiveness of an antidepressant drug on men and women. Problem 3 involves probabilities related to recidivism rates under a proposed new criminal law. Problem 4 asks about probabilities related to flipping biased coins. Problem 5 asks about probabilities related to selecting balls from buckets of different weights.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    123 views2 pages

    STAT7055 Spring Session 2017 Topic 2 Tutorial Questions

    Uploaded by

    Callum Lowe
    This document contains 5 statistics problems related to probability. Problem 1 asks about the probability that a car will idle roughly given that each of its 4 spark plugs has a 90% chance of functioning properly. Problem 2 asks about the effectiveness of an antidepressant drug on men and women. Problem 3 involves probabilities related to recidivism rates under a proposed new criminal law. Problem 4 asks about probabilities related to flipping biased coins. Problem 5 asks about probabilities related to selecting balls from buckets of different weights.

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    Download as pdf or txt
    of 2

    STAT7055 Spring Session 2017

    Topic 2 Tutorial Questions


    1. (Keller 10e Ex 6.91) In a four-cylinder engine there are four spark plugs. If any one of
    them malfunctions, the car will idle roughly, and power will be lost. Suppose that for
    a certain brand of spark plugs, the probability that a spark plug will function properly
    after 5000 miles is 0.9. Assuming that the spark plugs operate independently, what is
    the probability that the car will idle roughly after 5000 miles?

    2. (Keller 10e Ex 6.89, 6.90) The effect of an antidepressant drug varies from person to
    person. Suppose that the drug is effective on 80% of women and 65% of men. It is
    known that 66% of the people who take the drug are women.
    (a) What is the probability that the drug is effective?
    (b) Suppose you are told that the drug is effective. What is the probability that the
    drug taker is a man?

    3. (Keller 10e Ex 6.94) In Canada, criminals are entitled to parole after serving only one-
    third of their sentence. Virtually all prisoners, with several exceptions including mur-
    derers, are released after serving two-thirds of their sentence. The government has
    proposed a new law that would create a special category of inmates based on whether
    they had committed crimes involving violence or drugs. Such criminals would be subject
    to additional detention if the Correction Services judge them highly likely to re-offend.
    Currently, 27% of prisoners who are released commit another crime within 2 years of
    release. Among those who have re-offended, 41% would have been detained under the
    new law, where 31% of those who have not re-offended would have been detained.
    (a) What is the probability that a prisoner who would have been detained under the
    new law does commit another crime within 2 years?
    (b) What is the probability that a prisoner who would not have been detained under
    the new law does commit another crime within 2 years?

    4. Suppose I have four fair coins, two which have a head on both sides, one which has a
    tail on both sides, and one which is normal (a head on one side and a tail on the other
    side).
    (a) I shut my eyes, pick one of the four coins at random, and flip it. What is the
    probability that the lower face of the coin is a head?
    (b) I open my eyes and see that the coin is showing heads (on the upper face). What
    is the probability that the lower face is a head?

    5. (Topic 2 Example 4) There are three buckets that weigh 1kg, 2kg and 3kg, respectively.
    A bucket weighing ikg contains i white balls and 5 − i black balls, for i = 1, 2, 3. For
    example, the bucket weighing 1kg contains 1 white ball and 4 black balls. Suppose a
    bucket is chosen with probability proportional to its weight and two balls are randomly
    selected (without replacement) from this bucket.

    Page 1 of 2
    STAT7055 Spring Session 2017 Topic 2 Tutorial

    (a) Find the probability that both balls selected are white.
    (b) If both balls selected are white, what is the probability that the bucket weighing
    3kg was chosen?

    Page 2 of 2

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