3.1 Problems on conditional probability  (Page 2/3)

Four persons are to be selected from a group of 12 people, 7 of whom are women.

1. What is the probability that the first and third selected are women?
2. What is the probability that three of those selected are women?
3. What is the (conditional) probability that the first and third selected are women, given that three of those selected are women?

Twenty percent of the paintings in a gallery are not originals. A collector buys a painting. He has probability 0.10 of buying a fake foran original but never rejects an original as a fake, What is the (conditional) probability the painting he purchases is an original?

Five percent of the units of a certain type of equipment brought in for service have a common defect. Experience shows that 93 percent of the units with this defectexhibit a certain behavioral characteristic, while only two percent of the units which do not have this defect exhibit that characteristic.A unit is examined and found to have the characteristic symptom. What is the conditionalprobability that the unit has the defect, given this behavior?

A shipment of 1000 electronic units is received. There is an equally likely probability that there are 0, 1, 2, or 3 defective units in the lot. If one is selectedat random and found to be good, what is the probability of no defective units in the lot?

Data on incomes and salary ranges for a certain population are analyzed as follows. $S_1=$ event annual income is less than $25,000; $S_2=$ event annual income is between $25,000 and $100,000; $S_3=$ event annual income is greater than $100,000. $E_1=$ event did not complete college education; $E_2=$ event of completion of bachelor's degree; $E_3=$ event of completion of graduate or professional degree program. Data may be tabulated as follows: $P\left(E_1\right)=0.65,P\left(E_2\right)=0.30$ , and $P\left(E_3\right)=0.05$ .

1. Determine $P\left(E_3{S}_3\right)$ .
2. Suppose a person has a university education (no graduate study). What is the (conditional) probability that he or she will make $25,000 or more?
3. Find the total probability that a person's income category is at least as high as his or her educational level.

In a survey, 85 percent of the employees say they favor a certain company policy. Previous experience indicates that 20 percent of those who donot favor the policy say that they do, out of fear of reprisal. What is the probability that an employee picked at random really does favorthe company policy? It is reasonable to assume that all who favor say so.