Exam 4: Introduction to Probability

In a horse race,nine horses are running.Assume you have purchased a Trifecta ticket.(In Trifecta,the player selects three horses as first,second,and third place winners.To win,those three horses must finish the race in the precise order the player has selected. )How many possibilities of a Trifecta exist?

Records of a company show that 20% of the employees have only a high school diploma;70% have bachelor degrees;and 10% have graduate degrees.Of those with only a high school diploma,10% hold management positions;whereas,of those having bachelor degrees,40% hold management positions.Finally,80% of the employees who have graduate degrees hold management positions. a.What percentage of employees holds management positions? b.Given that a person holds a management position,what is the probability that she/he has a graduate degree?

A machine is used in a production process.From past data,it is known that 97% of the time the machine is set up correctly.Furthermore,it is known that if the machine is set up correctly,it produces 95% acceptable (non-defective)items.However,when it is set up incorrectly,it produces only 40% acceptable items. a.An item from the production line is selected.What is the probability that the selected item is non-defective? b.Given that the selected item is non-defective,what is the probability that the machine is set up correctly?

Events A and B are mutually exclusive with P(A)= 0.3 and P(B)= 0.2.Then,P(B^c)=

Assume your favorite football team has 2 games left to finish the season.The outcome of each game can be win,lose or tie.The number of possible outcomes is

In a recent survey of computer ownership,73.4% of the respondents indicated they own PC computers,while 21.8% indicated they own both PC and Mac computers,and 80.1% said they own at least one of the two computers. a.What is the probability that a respondent owns a Mac computer? b.Given that a respondent owns a PC,what is the probability that the respondent also owns a Mac? c.Are events "P" and "M" mutually exclusive? Why or why not? Explain using probabilities. d.Are the two events "P" and "M" independent? Explain,using probabilities.

A six-sided die is tossed 3 times.The probability of observing three ones in a row is

If A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5,then P(A $\cup$ B)=

A company plans to interview 10 recent graduates for possible employment.The company has three positions open.How many groups of three can the company select?

If A and B are independent events with P(A)= 0.05 and P(B)= 0.65,then P(A | B)=

If A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5,then P(A $\cap$ B)=

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn,what is the probability of drawing a black ace?

Since the sun must rise tomorrow,then the probability of the sun rising tomorrow is

A sample point refers to the

Assume you are taking two courses this semester (A and B).The probability that you will pass course A is 0.835,the probability that you will pass both courses is 0.276.The probability that you will pass at least one of the courses is 0.981. a.What is the probability that you will pass course B? b.Is the passing of the two courses independent events? Use probability information to justify your answer. c.Are the events of passing the courses mutually exclusive? Explain.

Records of a company show that 15% of the employees have only a high school diploma (H),75% have bachelor degrees (B),and 10% have graduate degrees (G).Of those with only a high school diploma,12% hold management positions;whereas,of those having bachelor degrees,58% hold management positions.Finally,82% of the employees who have graduate degrees hold management positions. a.What percentage of employees holds management positions? b.Given that a person holds a management position,what is the probability that she/he has a graduate degree?

If two events are mutually exclusive,then their intersection

If P(A)= 0.4,P(B | A)= 0.35,P(A $\cup$ B)= 0.69,then P(B)=

Assume you have applied for two scholarships,a Merit scholarship (M)and an Athletic scholarship (A).The probability that you receive an Athletic scholarship is 0.18.The probability of receiving both scholarships is 0.11.The probability of getting at least one of the scholarships is 0.3. a.What is the probability that you will receive a Merit scholarship? b.Are events A and M mutually exclusive? Why or why not? Explain. c.Are the two events A,and M,independent? Explain,using probabilities. d.What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? e.What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?

If A and B are independent events with P(A)= 0.4 and P(B)= 0.6,then P(A $\cap$ B)=