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Basic probability of different events occurring

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8. A sample of 2,000 licensed drivers revealed the following number of speeding violations.
Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000

a. What is the experiment?
b. List one possible event.
c. What is the probability that a particular driver had exactly two speeding violations?
d. What concept of probability does this illustrate?

66. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:
Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500
a. What is the probability of selecting a female student?
b. What is the probability of selecting a finance or accounting major?
c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
d. Are gender and major independent? Why?
e. What is the probability of selecting an accounting major, given that the person selected is a male?
f. f. Suppose two students are selected randomly to attend a lunch with the president of the university. What is the probability that both of those selected are accounting majors?

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The solution gives the step by step method to solve two basic problems in probability.

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Basic Probability Problems

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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