Question 1057669: A sample of two balls is drawn from an urn containing 2 white and 3 red balls. Suppose A and B are two events, described as
A = sample contains at least one white ball
B = sample contains balls of both colors
Determine if A and B are independent events.
I figured that the Probability of A is .7 and I'm unsure if the probability of B is either .3 or .6, but how do you figure out if they're independent or not?
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! P(A) = P(white, red) + P(red, white) + P(white, white) = (2/5)(3/4) + (3/5)(2/4) + (2/5)(1/4) = 14/20 = 0.70
P(B) = P(white, red) + P(red, white) = (2/5)(3/4) + (3/5)(2/4) = 12/20 = 0.60
P(A and B) = P(at least one white, and one of each color) = P(white, red) + P(red, white) = P(B) = 0.6
If the two events are independent, then P(A and B) = P(A) * P(B).
P(A) * P(B) = 0.7 * 0.6 = 0.42 ≠ 0.6
Thus, P(A and B) ≠ P(A) * P(B), so the two events are not independent.
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