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?

The probability that a newly designed electronic component will survive a given shock test is 5/6. Find the probability that exactly 3 of the next 4 components tested survive. 

 A company has installed 10,000 electric lamps in a metro. If these lamps have an average life of 1,000 burning hours with a S.D. of 200 hours. Assuming normality, what number of lamps might be expected to fail. 

i)  in the first 800 burning hours. 

ii) between 800 and 1200 burning hours.        

iii) more than 1000 burning hours  

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.

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?

Three technicians X, Y and Z service respectively 20%, 30% and 50% breakdowns when occur on an automated production line. The technician X makes an incomplete repair 1 time in 20, Y makes an incomplete repair 1 time in 10 and Z makes an incomplete 1 time in 15. For the next breakdown a repair made was found to be incomplete, find the probability that this repair was made by technician 

(i) X, 

(ii) Y, and  

(iii) Z  

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.