SOLUTION: A company has a 20-person grievance committee. When a grievance is filed, three of these 20 people are chosen at random to serve on a hearing panel. Suppose that two committees ar

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Question 1200581: A company has a 20-person grievance committee. When a grievance is filed, three of these
20 people are chosen at random to serve on a hearing panel. Suppose that two committees are
formed. What is the probability that these committees have at least one member in common?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
A company has a 20-person grievance committee. When a grievance is filed, three of these
20 people are chosen at random to serve on a hearing panel. Suppose that two highlight%28cross%28committees%29%29 panels are
formed. What is the probability that these highlight%28cross%28committees%29%29 panels have at least one member in common?
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First  panel can be formed in  C%5B20%5D%5E3 = %2820%2A19%2A18%29%2F%281%2A2%2A3%29 = 1140 different ways.

Second panel can be formed in  C%5B20%5D%5E3 = %2820%2A19%2A18%29%2F%281%2A2%2A3%29 = 1140 different ways.


Two panels can be formed in  C%5B20%5D%5E3%2AC%5B20%5D%5E3 = 1140%5E2 different ways.    (1)


Two panels that are not intersect (have empty intersections) can be formed in 

    C%5B20%5D%5E3%2AC%5B20-3%5D%5E3 = C%5B20%5D%5E3%2AC%5B17%5D%5E3 = 1140*680 different ways.          (2)


The probability that two panels have no intersection (have empty intersection) 
is the ratio of number (2) to number (1)

    P = %281140%2A680%29%2F%281140%2A1140%29 = 680%2F1140 = 34%2F57 = 0.5965  (rounded).  


The probability under the problem's question is the COMPLEMENT to it 

    P' = 1 - 0.5965 = 0.4035.    ANSWER

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The probability that the first person chosen for the second panel is not on the first panel is 17/20.
The probability that the second person chosen for the second panel is not on the first panel is 16/19.
The probability that the third person chosen for the second panel is not on the first panel is 15/18.

So the probability that none of the three people chosen for the second panel are on the first panel is (17/20)(16/19)(15/18) = 0.5965 (rounded).

Then the probability that at least one member of the second panel is on the first panel is 1-0.5965 = 0.4035.

ANSWER: 0.4035