The telephone lines serving an airline reservation office...

The telephone lines serving an airline reservation office are all busy about $60 \%$ of the time. a. If you are calling this office, what is the probability that you will complete your call on the first try? The second try? The third try? b. If you and a friend must both complete calls to this office, what is the probability that a total of four tries will be necessary for both of you to get through?

Transcript

0:00 Hello students.

00:01 Today we will discuss about this question.

00:03 In this question we are given that telephone line servings and airline reservation office that are busy about 60 percentage of the time.

00:14 Now here in the part a if you are calling this office what is the probability that you will complete your call in the first try? so here first try that is equal to question mark.

00:28 Second type probability of second try that is equal to question mark and probability of the third try that is equals to question mark in the part b if you and a friend must both complete calls in this office what is the probability that the total of four trials that will be total four trials that will be necessary for you to get through that is equals to question mark so here first of all let q, that will be the number of the telephone line servings and an airline reservation office that will be busy.

01:08 So therefore, this is given as q that is equals to 60 percentage that is equals to 0 .6.

01:14 Let p, that will be the telephone line servings and airline airline reservation office that will not be busy.

01:23 So that is p is equals to 1 minus q that is equals to 0 .4.

01:27 Now in the part a, we need to find the probability that you will complete the call in the first trial.

01:33 So, therefore, this is probability of y is equals to 1.

01:37 That is possible only when the first trial has the telephone line servings and the airline reservation office that will not be busy.

01:49 So, p of y that here we can say that p of y that is equals to y minus 1, r minus 1, p p -p -raised to r multiplied by 1 minus p raised to y minus r where y is equal to r r plus 1 and here 0 less than or equals to p less than or equals to 1.

02:11 Here random variable y is said to have a negative binomial probability distribution.

02:17 So therefore here probability of y is equal to 1 that is equals to 0 .4.

02:22 This will be the answer for the first trial.

02:25 Now here we need to find the probability of y is equals to 2...

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