Ms. X thinks that there is a 30% chance that her company will set up a branch office in New Delhi. If it is so, then she is 60% certain that she will be assigned the responsibilities of a branch manager there. What is the probability that Ms. X will be branch manager at the New Delhi office?

 The metro trains on a certain section run every 10 minutes between 5 a.m. to 10 p.m. What is the probability that a commuter entering the station at a random time during this period will have to wait  

(i) at least five minutes?

(ii) zero minute? 

(iii) 2 to 5 minutes?

 A bag contains 5 balls which are numbered from 1 to 5. Two balls are drawn without replacement from this. Find the expectation of the sum of the numbers on these balls.

A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them are Ambassadors, and (iii) all 5 are of the same make?

The joint density function of random variables X and Y is given by  

Are X and Y independent?
 

The distribution function F of a continuous variable is given by

F(x) = 0, if x < 0

= x 2 , if 0 < x < 1

= 1, if x > 3

(i) Find the pdf of X,

(ii) Evaluate P[|X| <1/ 2], using distribution function F,

(iii) Evaluate P[|X| < 1/ 2], using pdf.

The probability that a person living in a certain city owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.