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In a sample of 587 customers, 308 say they are happy with the service. If you...

In a sample of 587 customers, 308 say they are happy with the service. If you select three customers without replacement for a commercial, what is the probability they will all say they are happy with the service?

math   Statistics-And-Probability   
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Answer #1

GIVEN:

Total customers in the sample (T)= 587

Number of customers happy with services (H)= 308

Let,

P(H) be the probability of choosing a happy customer at a given time.

TO FIND:

In selecting 3 customers without replacement, the probability that they all will be happy.

SOLUTION:

probability that all 3 will be happy = (probability that 1st person will be happy) * (probability that 2nd person will be happy) * (probability that 3rd person will be happy) ------------(1)

now,

probability that 1st person will be happy = H / T = 308/587

now T1= 587-1=586 and H1 = 308-1= 307

thus, probability that 2nd person will be happy= H1/T1 =307/586

now T2=586-1=585, H2=307-1=306

thus, probability that 3rd person will be happy =H3/T3 = 306/585

Now in (1),

probability that all 3 will be happy

308 307 306 587 586 585

0.14378677238 0.1438

Clearly, the probability they will all say they are happy with the service is 0.1438

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