SOLUTION: In a sample of 350 customers, 125 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that

Question 1123451: In a sample of 350 customers, 125 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?
Can this be explained so I can use the explanation to answer future questions
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let's say you have things, of which would be considered successful selections. Then the probability of making a successful selection on the first try would simply be . But if you don't replace the thing selected on the first try, you no longer have things of which would be considered successful, you now have things of which would be successful, and the probability for the second try would be .

Since by adjusting the number of items and the number of successes you have made the two tries completely independent events, the probability of both is the product of the two individual probabilities.

So, for your problem:

You can do your own arithmetic

Extra Credit:

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability that the first person says service is poor is 125 / 350.

given that the first person says service is poor, then you have 124 people left who say service is poor out of 349 people who are left.

the probability that the second person says service is poor, given that the first person said that service is poor, is therefore 124 / 349.

the probability that both said service is poor is therefore 125 / 350 * 134 / 349.

here's a reference you might find useful.

http://www.probabilityformula.org/probability-without-replacement.html
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