An interviewer is given a list of people she can interview....

An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability $\frac{2}{3},$ what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people on the list?

Transcript

00:01 We know that a binaural distribution describes the possible number of times that a particular event will occur in a sequence of observation also we know that a trial has only two possible outcomes namely success or failure there is fixed and numbers of identical trials the trials of the experiment are independent of each other the probability distribution function of binaural distribution is bxxxion.

00:35 I'm a variable distribution is bxxx is equal to x is equal to n x p to the power x into 1 minus p to the power n minus x here n is the number of people that need to be interviewed and p is the probability that person agrees to agrees for interview and 1 minus p represents the probability that person do not agree for interview now we will solve question part a the probability that person the probability that person independently agrees to be interviewed is p equal to 2 by 3 the total number of people that need to be interviewed is x equal to 5 the probability the number of people in the list n is equal to 5 this is total number of people that need to be interviewed and the number of people in the list n equal to five the probability that the list contain five people to be interviewed is px is equal to five is equal to five c five into two by three to the power 5 into 1 minus 2 by 3 to the power 5 minus 5 solving this we will get 0 .13172 hence the probability that an interviewer speaks to five people is 0 .13172 also this is equivalent to 13 .17 percent hence there is 13.

03:21 Point one seven percent chance that an interviewer speaks to five people now we will solve question part b the probability of person independently agrees to interviewed is b is equal 2 by 3 we know that and the total number of people that need to be interviewed is x equal to 5 here the number people in the list and is equal to 8 the probability that the list contain five people to be interviewed is p x equal to 5 this is equal to 8 5 into 2 by 3 to the power 5 into 1 minus 2 by 3 to the power 8 minus 5 solving this we will get 0 .27 312 hence there is 27 .3...

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