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Answer on Statistics and Probability Question for abdallah hussien

Question #13311
a box contains 8 red,3 white and 9 blue balls if three balls are drawn without replacement determine the probability
a)all three are red
b)two are red and one is white
c)all three are white
d)at least one is white
e)one for each color is drawn
Expert's answer
There are 8+3+9 = 20 balls in a box.
p{r} = 8/20 = 0.4;
p{w} = 3/20 = 0.15;
p{b} = 9/20 = 0.45;

a. P = 8/20 * 7/19 * 6/18 = 336/6840 = 14/285 ( = C(8,3)/C(20,3) );
b. P = (C(8,2) + C(3,1)) / C(20,3) = 31/1140;
c. P = 3/20 * 2/19 * 1/18 = 6/6840 = 1/1140 ( = C(3,3)/C(20,3) );
d. P = (C(3,1) + C(19,2))/C(20,3) = 174/1140 = 87/570;
e. P = p{r}p{w}p{b} = 0.4*0.15*0.45 = 0.027.

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