Question 1025315: A crate contains six housings that have uniquely 1,2,3,4,5, and 6 defects. Two housings are drawn at random from the crate without replacement. Let the random variable X be equal to the larger of the two numbers of defectives on the two housings. What is the probability distribution of X?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Look at the possible 30 outcomes,
(1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5)
Then the max value of the pair,
2 3 4 5 6
2 3 4 5 6
3 3 4 5 6
4 4 4 5 6
5 5 5 5 6
6 6 6 6 6
The number of occurences of each number,
1=>0
2=>2
3=>4
4=>6
5=>8
6=>10
So then the probability distirubtion is,
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