SOLUTION: In a shop there are 20 customers, 18 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase?

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Question 149493: In a shop there are 20 customers, 18 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase? Is it 0.7717, 0.7605, 0.8524, or 0.8808.
Please help
Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
In a shop there are 20 customers, 18 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase? Is it 0.7717, 0.7605, 0.8524, or 0.8808.
Please help 


It's not any of those.  It's 0.7158

P(1st chosen will purchase 

      AND 

           2nd chosen will purchase 

                  AND

                      3rd chosen will purchase)

                            =

P(1st chosen will purchase) 

TIMES

P(2nd chosen will purchase, given that the 1st chosen will purchase)

TIMES

P(3rd chosen will purchase, given that the 1st and 2nd chosen will purchase)

=

 or rounded to ten-thousandths,

.

You can also do it using combinations: 



=

 

Stanbon's solution is incorrect because 
the choices are not independent. Binomial
probabilities are ONLY for independent choices.
The choices are not independent because the 
probability of selecting the second one as a 
purchaser CHANGES after selecting the first one. 
Also the probability of selecting the third one 
as a purchaser CHANGES after selecting the 
first two.

Edwin
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
In a shop there are 20 customers, 18 of whom will make a purchase.
-----------
P(a random person in the group makes a purchase) = 18/20 = 9/10
-----------------
If three customers are selected, one at a time, at random, what is the probability that all will make a purchase?
-----------------
This is a binomial problem with p=0.9
P(3 of 3 make a purchase) = 0.9^3 = 0.729
------------
Cheers,
Stan H.




Is it 0.7717, 0.7605, 0.8524, or 0.8808.

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