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    Probability Problems

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    1) A shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment, but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24 hour period, what is the expected gain per package?

    2) A study of the behavior of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a 2 year period after treatment may depend on the offender's education. The proportion of the total number of cases that fall into 4 Education/Conviction categories are shown in the table below:
    Status within 2 years After Treatment
    Education Convicted Not Convicted Totals
    10yrs or more .10 .30 .40
    9yrs or less .27 .33 .60
    Totals .37 .63 1.00

    Suppose a single offender is selected from the treatment program. Here are the events of interest:

    A. The offender has 10 or more years of education.
    B. The offender is convicted within 2 years after completion of treatment.

    Find the appropriate probabilities for these events:
    1) A
    2) B
    3) A intersection B
    4) A Union B
    5) A Complement
    6) Complement of A union B
    7) Complement of A Intersection B
    8) A given that B has occurred
    9) B given that A has occurred

    3) Accident records collected by an automobile insurance co. give the following information:
    The probability that an insured driver has an automobile accident is .15; If an accident has occurred, the damage to the vehicle amounts to 20% of its market value with probability .80, 60% of its market value with probability .12, and a total loss with probability .08.

    What Premium should the Insurance Company charge on a $22,000 car so that the expected gain by the company is 0?

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    https://brainmass.com/statistics/probability/33960

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    1) A shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment, but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24 hour period, what is the expected gain per package?

    Profit made when package delivered= $0.70 =15.5-14.8
    Loss made when package not delivered= -$14.80 =Cost

    Probability Profit/loss Prob X Profit
    package delivered 0.98 $0.70 $0.69
    package not delivered 0.02 -$14.80 -$0.30
    Expected gain = Total= $0.39

    Expected gain per package= $0.39

    2) A study of the behavior of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a 2 year period after treatment may depend on the offender's education. The proportion of ...

    Solution Summary

    There are answers to 3 questions on probability

    $2.19