Probability Distribution Table Question?

Question

A box contains 25 balls, 10 are blue and 15 are red. Lest x denote the number of blue balls in a random sample of 3 balls (sampling without replacement). Construct a probability distribution table for the variable x, and calculate the expected value of x.

Appreciate the help :)

Answer 1

P(0 red & 3 blue) = (10C3) / (25C3) = 120/2300 = .0521
P(1 red & 2 blue) = (15C1)*(10C2) / (25C3) = 15*45/2300 = .2935
P(2 red & 1 blue) = (15C2)*(10C1) / (25C3) = 105*10/2300 = .4565
P(3 red & 0 blue) = (15C3) / (25C3) = .1978

expected value = 3*.0521 + 2*.2935 + 1*.4565 + 0*.1978 = 1.2

Answer 2

P(X=0) = (3*7*13)/(5*12*23) = 0.197826
P(X=1) = (3*7)/(2*23) = 0.456522
P(X=2) = (3*3*3)/(4*23) = 0.293478
P(X=3) = (2*3)/(5*23) = 0.052174
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E(X) = 0*0.197826 + 1*0.456522 + 2*0.293478 + 3*0,052174 = 1.2
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