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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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There are answers to 3 questions on probability

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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 ...

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