Statistics for Economics : Assignment 1
1. A delegation of three needs to be chosen from assistant professors in the economics
department (numbering ten) to represent the department at a university-level event.
In how many ways:
(a) Can the delegation be chosen?
(b) Can it be chosen, if two people refuse to go together?
(c) Can it be chosen, if two particular members insist on either both going or neither
going?
(d) Can it be chosen, if two people must be chosen from full-time assistant profes-
sors (six in number) and one person must be chosen from the visiting assistant
professors (four in number)?
2. A university in Haryana has smoking alarms in all the student residence halls. The
smoking alarm has 99% probability of accurately detecting if someone is truly smoking
and 0.1% probability of wrongly detecting if someone is not smoking. Suppose there
are 10 students out of a total 2000 students in the University who smoke in the hostel
room without tampering the smoke alarm. Now, suppose smoke alarm detected that
someone smoked early in the morning of 16 August in room no.007. Then, what is the
probability that someone was truly smoking in that room?
(a) Suppose all the rooms are single occupancy.
(b) Suppose all the rooms are double occupancy.
3. Suppose five percent men and 0.25 percent women are colour-blind. A colour-blind
person is chosen at random. What is the probability of this person being male? Assume
that there are an equal number of males and females. What if there were twice as many
males as females?
4. 4 PhD students share a common workplace in a university of Haryana. But they have
their own preference regarding whether to switch on the common AC or not. Suppose
student A first enters the workplace and switches on the AC with a probability of 2
3.
After her, student B, C and D enter sequentially. Each of them has 2
3probability of
changing the AC status (switch on/off) and 1
3probability of leaving it unchanged.
(a) Find the probability of finding the AC switched on at the end if student A didn’t
switch it on.
(b) Find the probability that student B switched off the AC if the AC was switched
on at the end.
5. You and your friends have rented a car for an 8,000 mile cross-country road trip. Your
rental car may be of three different types: brand new, nearly 1 year old, or a lemon
(bound to break down). Now, if the car you received is brand new, then the probability
that it will break down is 0.05; if it is 1 year old, it will break down with probability
1
