Question 1166979: Suppose that you have 7 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places.
G1 = the first card drawn is green
G2 = the second card drawn is green
a. P(G1 and G2) =
b. P(At least 1 green) =
c. P(G2|G1) =
d. Are G1 and G2 independent?
They are independent events
They are dependent events
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! for both green it is (7/12)(7/12) with replacement or 49/144, or 0.3403.
at least 1 green is 1-0 green probability. For 0 green for both cards it is (5/12)^2 or 25/144, so the answer is 119/144 or 0.8264 probability.
That is also the 0.3403 above + 2 (7/12)(5/12) or 70/144 or 0.4861
That plus 0.3403 is 0.8264.
Given G1 is green the probability G2 is green is 7/12 with replacement. Nothing has changed, and the trials would be independent, in that what happened on the first doesn't affect the second.
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