a radio station staff writes the phone numbers of eight fina

a radio station staff writes the phone numbers of eight finalists on separate slips of paper and places them in a hat. Two phone numbers are from listeners in the rural region, 2 phone numbers from listeners in the suburbs and 4 phon numbers from city listeners. An experiment consists of randomly selecting one slip of paper from the eight slips in the hat. If the experiment is carried out three times, replacing the number drawn each time for the next drawing what is the probability of

a. All three slips containing city phone numbers

b. None of the slips containing the phone number of a listener from the suburbs.

Solution

let

R be event that slip containing rural reagion phone number

S be event that slip containing phone number from suburban reagion

C be event that slip containing phone number from city

n(R)=2 n(S)=2 n(C)=4

N=8

as we done experiment with replacement hence probability of each event is same each time

a) hence

probability of getting slip containing city phone number for first time =P(C)=4/8=0.5

as we draw slip with replacement

hence required probability that All three slips containing city phone numbers=0.5*0.5*0.5=0.125

b)probability of does not getting slip that contain suburbon reagion phone number for first time

=1-P(S)=P(RUC)=6/8=0.75

as all three slips drawn with replacement then

required probability that None of the slips containing the phone number of a listener from the suburbs=0.75*0.75*0.75 =0.421875