Answer to Question #370 in Statistics and Probability for Alex Landon
The results of the two described extractions are not dependent on each other, hence the probability of getting two blue buttons (a blue button at the first extraction and a blue button at the second extension) is: P(blue) = P(blue, 1)*P(blue, 2) = (6/16)*(5/15) = 30/(16*15) = 1/8.
Similarly for the red buttons:
P(red, 1) = 10/(10+6) = 10/16;
P(red, 2) = (10-1)/(10+6-1) = 9/15;
P(red) = P(red, 1)*P(red, 2) = (10/16)*(9/15) = 90/(16*15) = 3/8.
Getting two buttons of the same color is equivalent to getting two red or two blue buttons. As these events are independent, the probability of extracting two buttons of the same color is:
P(blue or red) = P(blue) + P(red) = 1/8 + 3/8 = 4/8 = 1/2.
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