SOLUTION: eith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 7 have brake problems. A

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Question 1119808: eith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 7 have brake problems. A sample of 6 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes? (Round your answer to 4 decimal places.)
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This would be 6C2*9C5, the number of ways 6 can have 2 with brake problems * the number of ways the other 9 would have 5 brake problems.
Denominator is 15C7 (the sum of the 6 and 9 and the 2 and 5.
This is 1890/6435 or 0.2937
Another way is to take a sample of 6 with 2
7/15*6/14*8/13*7/12*6/11*5/10=70560/(15*14*13*12*11*10)=0.0196. There are 15 of these ways where 2 will have brake problems and where the numerator is ordered differently but with the same numbers, so all 15 is 0.2937.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Keith's Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements
in the Greenville, South Carolina, area. Of these 15 trucks, 7 have brake problems.
A sample of 6 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes?
(Round your answer to 4 decimal places.)
~~~~~~~~~~~~~~~~~~~~~~ 

This probability is this ratio  .


We start choosing 2 defective cars among of 7 defective. It can be done in  =  = 21 ways.


We complement 2 defective cars to 6 by adding 4 regular cars from 8 = 15-7 regular cars.  It can be done by  =  = 70 ways.


The total number of ways to choose 6 cars of 15 is   =  = 5005.


Thus the probability under the question is   = 0.2937 = 29.37%.


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