SOLUTION: Two balls are drawn in succession without replacement from a box containing 4 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Constr

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Question 1101386: Two balls are drawn in succession without replacement from a box containing 4 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability distribution of the random variable Z.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
First determine the probabilities of the events.

  events           Probability
    RR          (4/10)(3/9) = 2/15
    RB          (4/10)(6/9) = 4/15
    BR          (6/10)(4/9) = 4/15 
    BB          (6/10)(5/9) = 1/3

The probability of 0 blue balls (RR)is 2/15
The probability of 1 blue ball is (RB or BR) is 4/15+4/15 = 8/15
The probability of 2 blue balls (BB) is 1/3

So the probability distribution is:

Z   p(Z)
--------   
0   2/15
1   8/15
2   1/3

Notice that the sum of the probabilities = 2/15+8/15+1/3 = 1

Edwin