Acomputer lab has two printers. printer i handles 40% of all the jobs. its printing time is exponential with the mean of 2 minutes. printer ii handles the remaining 60% of jobs. its printing time is uniform between 0 minutes and 5 minutes. a job was printed in less than 1 minute. what is the probability that it was printed by printer i?

 0.3042

Explanation:

Let A  and B are the events to that job done by Printer I and Printer II respectively.

Given : P(A)=0.40    P(B)=0.60

Printing time of Printer I is Exponential with the mean of 2 minutes.

i.e. average number of job done in one minute:

The cumulative distribution function (CDF) for exponential distribution:-

, where is the mean.

Then, the cumulative distribution function (CDF) for Printer I:-

i.e.

Printing time of Printer II is Uniform between 0 minutes and 5 minutes.

The cumulative distribution function  (CDF) for uniform distribution in interval (a,b) :-

Then,

i.e.

Now, the required probability :-

Hence, the required probability = 0.3042