SOLUTION: Suppose your top drawer contains different colored socks: 6 are white, 8 are black, 16 are pink, and 12 are blue. All socks in the drawer are loose (unpaired). In the morning, you

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose your top drawer contains different colored socks: 6 are white, 8 are black, 16 are pink, and 12 are blue. All socks in the drawer are loose (unpaired). In the morning, you       Log On


   

Question 1050817: Suppose your top drawer contains different colored socks: 6 are white, 8 are black, 16 are pink, and 12 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction.
(a) What is the probability that you get a blue pair of socks?

(b) What is the probability that you do not get a blue pair of socks?

(c) What is the probability that you get either a white pair or a blue pair of socks?

(d) What is the probability that you get one black sock and one white sock?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Total 42 : 6 are white, 8 are black, 16 are pink, and 12 are blue
P(2B) = (12/42)(11/41)
P(not 2B) = 1 - (12/42)(11/41)
P(2W 0r 2B) = (6/42)(5/41) + (12/42)(11/41)
P(1Bl & 1W) = (8/42)(6/41) + (6/42)(8/41)
Multiply out and reduce fractions
Total 42 : 6 are white, 8 are black, 16 are pink, and 12 are blue
P(2B) = %2812%2F42%29%2811%2F41%29+=+132%2F1722 = 22/287
P(not 2B) = 1+-+%2812%2F42%29%2811%2F41%29+=+1+-+22%2F287+=265%2F287 = 265/287
P(2W 0r 2B) = %286%2F42%29%285%2F41%29+%2B+%2812%2F42%29%2811%2F41%29+=+162%2F1722 = 27/287
P(1Bl & 1W) = %288%2F42%29%286%2F41%29+%2B+%286%2F42%29%288%2F41%29+=+96%2F1722 = 16/287