# Basic Probability

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?

Testing the number of speeding violations per driver.

b. List one possible event.

46 drivers had one speeding violation.

c. What is the probability that a particular driver had exactly two speeding violations?

The probability that a particular driver had exactly two speeding violations is .009 found by 18/2000 = 0.009.

d. What concept of probability does this illustrate?

Empirical probability

Please check answers if they are correct ..if not please solve:

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?

P(F) = = 0.4

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?

P(Fm or A) = P(Fm) + P(A) - P (both Fm and A)

P(Fm or A) = 200/500 + 200/500 - 100/500

P(Fm or A) = .40 + .40 - .20

P(Fm or A) = .60

The probability of selecting a female or an accounting major is .60

Application used was Joint Probability.

d. Are gender and major independent? Why?

No because independence requires that P(A / B) = P(A)

In this case P(gender / major) = P(gender)

100/300 DOES NOT EQUAL 200/500

Joint Probability must be used

e. What is the probability of selecting an accounting major, given that the person selected is a male?

P(A and M) = P(A) P(M)

P(A and M) = = = .24

Probability of selecting an accounting major given the person selected is a male is .24.

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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#### Solution Summary

Probability problems related to empirical definition, addition theorem, joint probability, marginal probability and conditional probability.