1. Example: An automobile manufacturer provides vehicles equipped with selected options. Each vehicle is ordered; - with or without an automatic transmission, - with or without air conditioning - with one of three choices of a stereo system - with one of four exterior colors

2. BONUS: Consider the automobile manufacturer includes interior color as another option. There are four choices of interior color; red, black, blue or brown. However; - with a red exterior, only a black or red interior can be chosen - with a white exterior, any interior color can be chosen, - with a blue exterior, only a black, red or blue interior can be chosen - with a brown exterior, only a brown interior can be chosen. Q: Use tree diagram to determine # sample points

3. Example:
Consider a recent study conducted by the personnel manager of a major computer software company.
The study showed that 30% of employees who left the firm within two years did so primarily because they were dissatisfied with their salary, 20% left because they were dissatisfied with their work assignments, 12% of the former employees indicated dissatisfaction with both their salary and their work assignments.
Question:
What is the probability that an employee who leaves within two years does so because of dissatisfaction with salary, dissatisfaction with work assignment or both?

4. Assigning Probabilities
Basic Requirements for Assigning Probabilities
2. The sum of the probabilities for all experimental
outcomes must equal 1.
P(E1) + P(E2) P(En) = 1
where:
n is the number of experimental outcomes

5. Multiplication Law
The multiplication law provides a way to compute the
probability of the intersection of two events.
The law is written as:
P(A B) = P(B)P(A|B)

6. Mutual Exclusiveness and Independence
Do not confuse the notion of mutually exclusive
events with that of independent events.
Two events with nonzero probabilities cannot be
both mutually exclusive and independent.
If one mutually exclusive event is known to occur,
the other cannot occur.; thus, the probability of the
other event occurring is reduced to zero (and they
are therefore dependent).
Two events that are not mutually exclusive, might
or might not be independent.

7. Example-1:
An insurance company sells a 10,000 TRL 1-year term insurance policy at an annual premium of 290 TRL. Based on many year’s information, the probability of death during the next year for a person of customer’s age, sex, health etc. is 0.001
Q: What is the expected gain (amount of money made by the company) for a policy of this type?

8. Example:
Consider a recent study conducted by the personnel manager of a major computer software company.
The study showed that 30% of employees who left the firm within two years did so primarily because they were dissatisfied with their salary, 20% left because they were dissatisfied with their work assignments, 12% of the former employees indicated dissatisfaction with both their salary and their work assignments.
Question:
What is the probability that an employee who leaves within two years does so because of dissatisfaction with salary, dissatisfaction with work assignment or both?

9. Properties of the Binomial Probability Distributions
1- The experiment consists of a sequence of n identical trials
2- Two outcomes (SUCCESS and FAILURE ) are possible on each trial
3- The probability of success, denoted by p, does not change from trial to trial. Consequently, the probability of failure, denoted by q and equals to 1-p , does not change from trial to trial
4- The trials are independent.

10. According to a research only 5% of the cigarette smokers enter into a treatment program to help them quit smoking. In a random sample of 200 smokers, let x be the number who enter into a treatment program.
A-) Explain why x is a binomial r.v.
B-) What is the value of p? Interpret this value.
c-) What is the expected value of x? Interpret this value.

11. Example: Purchase Decision
Consider the purchase decisions of the next three customers who enter the clothing store. On the basis of past experience, the store manager estimates the probability that any one customer will make a purchase is 0.30
Q: What is the probability that two of the next three customers will make a purchase?

12. Example: Hourly Wages
According to a study in a certain city 50% of workers between the ages of 25 to 34 years were paid hourly rates of USD 10 or more in the year of 2003.
Find the probabilities that among 10 randomly selected workers in this category;
a-) At least five workers earned wages of USD 10 per hour or more
b-) At most five workers earned wages of USD 10 per hour or more
c-) Anywhere from 4 to 6 workers earned wages of USD 10 per hour or more

13. The Sales of Automobiles for 300 days
0 automobile sold
54 days
1 automobile sold
117 days
2 automobile sold
72 days
3 automobile sold
42 days
4 automobile sold
12 days
5 automobile sold
3 days
Total:
300 days