SOLUTION: 7 white socks and 4 black socks are in a bag. 2 socks are drawn without replacement. what is the probality that they are the same color? Write the answer as a reduced fraction.

Question 36376: 7 white socks and 4 black socks are in a bag. 2 socks are drawn without replacement. what is the probality that they are the same color? Write the answer as a reduced fraction.
Answer by Prithwis(166) (Show Source): You can put this solution on YOUR website!
P(Same color) = P(both are white) + P(both are black)
Both are white: White in the first draw and white in the second draw
P(both are white) = P(White in the first draw and white in the second draw)
= [C(7,1)/C(11,1)] *** Without Replacement ***
= (7/11)*(6/10) = 42/110 = 21/55;
P(both are black) = P(Black in the first draw and black in the second draw)
= [C(4,1)/C(11,1)] *** Without Replacement ***
= (4/11)*(3/10) = 12/110 = 6/55;
P(Same color) = P(both are white) + P(both are black)
=> P(Same color) = 21/55 + 6/55 = 27/55
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