Exam 4: Introduction to Probability

Assume you have applied to two different universities (let's refer to them as Universities A and B)for your graduate work.In the past,25% of students (with similar credentials as yours)who applied to University A were accepted,while University B accepted 35% of the applicants.Assume events are independent of each other. a.What is the probability that you will be accepted in both universities? b.What is the probability that you will be accepted to at least one graduate program? c.What is the probability that one and only one of the universities will accept you? d.What is the probability that neither university will accept you?

A very short quiz has one multiple choice question with five possible choices (a,b,c,d,e)and one true or false question.Assume you are taking the quiz but do not have any idea what the correct answer is to either question,but you mark an answer anyway. a.What is the probability that you have given the correct answer to both questions? b.What is the probability that only one of the two answers is correct? c.What is the probability that neither answer is correct? d.What is the probability that only your answer to the multiple choice question is correct? e.What is the probability that you have only answered the true or false question correctly?

Sixty percent of the student body at UTC is from the state of Tennessee (T),30% percent are from other states (O),and the remainder are international students (I).Twenty percent of students from Tennessee live in the dormitories,whereas,50% of students from other states live in the dormitories.Finally,80% of the international students live in the dormitories. a.What percentage of UTC students live in the dormitories? b.Given that a student lives in the dormitory,what is the probability that she/he is an international student? c.Given that a student lives in the dormitory,what is the probability that she/he is from Tennessee?

The probability of the occurrence of event A in an experiment is 1/3.If the experiment is performed 2 times and event A did not occur,then on the third trial event A

Of five letters (A,B,C,D,and E),two letters are to be selected at random.How many possible selections are there?

If P(A)= 0.48,P(A $\cup$ B)= 0.82,and P(B)= 0.54,then P(A $\cap$ B)=

Assume a businessman has 7 suits and 8 ties.He is planning to take 3 suits and 2 ties with him on his next business trip.How many possibilities of selection does he have?

If a dime is tossed four times and comes up tails all four times,the probability of heads on the fifth trial is

A lottery is conducted using three urns.Each urn contains chips numbered from 0 to 9.One chip is selected at random from each urn.The total number of sample points in the sample space is

From among 8 students how many committees consisting of 3 students can be selected?

Some of the CDs produced by a manufacturer are defective.From the production line,5 CDs are selected and inspected.How many sample points exist in this experiment?

As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year.There is a 0.72 probability that you will get a promotion,a raise,or both.The probability of getting a promotion and a raise is 0.25. a.If you get a promotion,what is the probability that you will also get a raise? b.What is the probability that you will get a raise? c.Are getting a raise and being promoted independent events? Explain using probabilities. d.Are these two events mutually exclusive? Explain using probabilities.

One of the basic requirements of probability is

Records of a company show that 15% of the employees have only a high school diploma;75% have bachelor degrees;and 10% have graduate degrees.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?

Each customer entering a department store will either buy or not buy some merchandise.An experiment consists of following 4 customers and determining whether or not they purchase any merchandise.How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser. )

If A and B are independent events with P(A)= 0.35 and P(B)= 0.20,then,P(A $\cup$ B)=

Two events with nonzero probabilities

How many committees,consisting of 3 female and 5 male students,can be selected from a group of 5 female and 8 male students?

If P(A)= 0.68,P(A $\cup$ B)= 0.91,and P(A $\cap$ B)= 0.35,then P(B)=

All the employees of ABC Company are assigned ID numbers.The ID number consists of the first letter of an employee's last name,followed by four numbers. a.How many possible different ID numbers are there? b.How many possible different ID numbers are there for employees whose last name starts with an A?