exercises for practice

7/28/2019 Exercises for Practice

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Suppose the entire cola industry produces only two colas viz., Pepsi and Coke.

Given that a person last purchased Pepsi, there is 90% that his next purchase

will be Pepsi. Given that a person last purchased Coke, there is an 80% that the

next purchase will be Coke.

i. If a person is currently a Coke purchaser, what is the probability that two

purchases from now he will purchase Pepsi ?

ii. If a person is currently a Pepsi purchaser, what is the probability that from

three purchases from now he will purchase Pepsi ?

According to a weather forecaster's subjective probability assessments (nobody believes

them!), the probability of record-breaking rain during this year in Jamshedpur is 0.01

(thank God!). However, if Ranchi has a record-breaking rain, the probability is 0.5 that

Jamshedpur will have a record-breaking rain. If Ranchi and Rourkela both have record-

breaking rain, the probability that Jamshedpur will have record-breaking rain is 0.8. The

probability that Ranchi will experience record-breaking rain if Rourkela experiences

record-breaking rain is 0.6. The probability that Rourkela will experience record-breaking rain is 0.02. (What the hell is the question, Sir?). What is the probability that all

three places will have record-breaking rain during this year?

(15)

A psychologist developed a test designed to help predict whether production-line

workers in a large industry will perform satisfactorily. A test was administered to all new

employees in a corporation. At the end of the first year of work, these employees were

rated by their supervisors: 18% were rated excellent, 53% were rated satisfactory and

29% were rated poor. 48% percent of those rated excellent passed the psychologists

test, as did 22% of those rated satisfactory and 12% of those rated poor.

a) What is the probability that a randomly selected employee will pass the

psychologists test?


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b) What is the probability that an employee who doesnt pass the test will be rated

excellent or satisfactory?

A Professor finds that he awards a final grade of A+

in QT to 20% of the

students.(Certainly can't be me!). Of those who obtain a final grade of A+, 70% obtained

an A+

in the mid-term examination. (Can't be you!!). Also, 10% of the students who

failed to obtain a final grade of A+

earned an A+

in the mid-term examination. What is

the probability that a student with an A+

in the mid term examination will obtain a final

grade of A+

?

The owner of TMH (Thumhari Marzi se Maro) Hospital wants to open a new facility in acertain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether

anticipated demand is low, medium or high. On the basis of his past experience, the

probabilities of low demand, Medium demand and high demand are estimated as 0.1,

0.4and 0.5 and the short-range payoffs in Rs are calculated as follows.

Demand Acts

Build 25 bed Build 50 bed Build 100 bed

Low 30,000 -20,000 -40,000

Medium 35,000 50,000 -10,000

High 40,000 55,000 75,000

1) What would be the best decision?

2) What is the value of Expected Value of Perfect Information?

The table given below shows the probabilities of investors categorised according to the

annual rate of return expected and the level of risk acceptable.


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Let X be the random variable denoting the expected annual rate of return (ARR) and Y be

the random variable denoting the acceptable level of risk(LOR).

X = 0 if the ARR < 10%

1 if the ARR is between 10%-15%

2 if the ARR >15%

let Y = 0 if the LOR is high

1 if the LOR is Medium

2 if the LOR is low

3 if the LOR is is none

Y \ X 0 1 2 Total

0 1/12 1/6 1/24

1 1/4 1/4 1/40

2 1/8 1/20 0

3 1/120 0 0

Total

Find

i. P( X=1 , Y=2)

ii. P(X+Y Y)

iv. COV(X,Y)

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