SOLUTION: A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x.

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Question 183159: A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A bag contains 23 cubes, of which 13 are red. Three cubes are drawn simultaneously, without replacement. Let x be the number of red cubes drawn. Find the expected value of x.
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Random Variable Values: 0,1,2,3
This is the number of red balls drawn
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Corresponding Probabilities:
P(x=0) = 10C3/23C3
P(x=1) = [13C1*10C2]/23C3
P(x=2) = [13C2*10C1]/23C3
P(x=3) = 13C3/23C3
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To calculate the "expected value",
Multiply each random variable value by its probability.
Then add up the 4 products.
That is the expected value of "x".
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[10C3/23C3]*0 = 0
[[13C1*10C2]/23C3]*1 = 0.3303
[[13C2*10C1]/23C3]*2 = 0.8807
[13C3/23C3]*3 = 0.4845
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Adding you get 0.3303+-8807+.4845 = 1.7
That is the expected value of "x".
Cheers,
Stan H.