1)A random sample of 500 households in Mumbai was selected and several variables were recorded for each household. Indicate
scale of the following variables.
1. Household Total Income
2. Primary Language used at home
3. Socio Economic Status coded as 1=low Income, 2= middle Income ,3= high Income
4. Rating Given by the Household to quality of a particular product
2) Define any two measures each of central tendency & dispersion and compute them for the data which gives values of air quality
index in different parts of Pune
28,42,58,48,45,55,60,49,50
3) Define coefficient of variation and use it to find out which of the following investment is more risky .
INVESTMENT A : A.M .of returns= 12% , S.D of returns : 2%
INVESTMENT B : A.M .of returns= 11% , S.D of returns : 1%
Probability and Probability Distributions: Basic Concepts of Probability: Addition theorem,Multiplication theorem,
1)Describe three approaches to probability : Classical Approach, Relative Frequency Approach & Subjective Probability
Approach
2)State addition theorem of probability and indicate when it is used.
3)State multiplication theorem of probability and indicate when it is used.
5) On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of
age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the
influence of alcohol.
Let A be the event that a driver is under the influence of alcohol.
Let Y be the event that a driver is less than 30 years old.
a.
b.
c.
d.
e.
f.
g.
Determine P(A) and P(Y).
What is the probability that a driver is under 30 and not under the influence of alcohol?
Given that a driver is not under 30, what is the probability that he/she is under the influence of alcohol?
What is the probability that a driver is under the influence of alcohol, when we know the driver is under 30?
Show the joint probability table.
Are A and Y mutually exclusive events? Explain.
Are A and Y independent events? Explain.
Answers:
a. P(Y) = 0.6
P(A) = 0.5
b. 0.2
c. 0.25
d. 0.667
e.
A
Ac
Y
0.4
0.2
Yc 0.1
0.3
f.
No, P(A  Y) 0
g. No, P(AY)  P(A)
6) A bank has the following data on the gender and marital status of 200 customers .
Single
Married
Male
20
100
Female
30
50
a. What is the probability of finding a single female customer?
b. What is the probability of finding a married male customer?
c. If a customer is female, what is the probability that she is single?
d. What percentage of customers is male?
e. If a customer is male, what is the probability that he is married?
f.
Are gender and marital status mutually exclusive?
g. Is marital status independent of gender? Explain using probabilities
Answers:
a. 0.15
b. 0.5
c. 0.375
d. 60%
e. 0.833
f.
No, the intersection is not zero.
g. They are not independent because P(male) = 0.6 P(malesingle) = 0.4
7)From among 8 students how many committees consisting of 3 students can be selected?
Answer: 56
8) From a group of seven finalists to a contest, three individuals are to be selected for the first and second and third places.
Determine the number of possible selections.
Answer: 210
9)
Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of
selections exist?
Answer: 90
10) 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.
b.
c.
d.
e.
What is the probability that you will receive a Merit scholarship?
Are events A and M mutually exclusive? Why or why not? Explain.
Are the two events A, and M, independent? Explain,using probabilities.
What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?
What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
Answers:
a. 0.23
b. No, because P(A  M)  0
c. No, because P(A  M)  P(A) P(B)
d. 0.4783
e. 0.6111