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probability

by ketkoag » Wed May 06, 2009 10:14 am
A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2
television sets are to be chosen at random from this shipment, what is the probability
that at least 1 of the 2 sets chosen will be a black-and-white set?
A. 1/7 B. ¼ C. 5/14 D. 11/28 E. 13/26
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by DanaJ » Wed May 06, 2009 10:29 am
IMHO there are two ways of tackling this. You should pick whichever pops up first on D-Day.

1. Think of possible combinations to get at least one black and white TV:
a. first TV is black and white, second TV is color: probability will be 2/8*6/7 = 1/4*6/7 = 6/28 = 3/14 (this is because for your first pick you have 2 favorable cases out of 8 and for your second pick you have 6 favorable cases out of 7).
b. second TV is black and white, first TV is color: probability will be 6/8*2/7 = 3/14 again.
c. both TVs are black and white: probability will be 2/8*1/7 = 1/28.

Add them up to get 2*3/14 + 1/28 = 13/28.

2. Notice that the probability of picking at least one black and white TV is the opposite op picking all color TVs. The probability of picking all color TVs will be 6/8*5/7 = 15/28, which means that your answer will be 1 - 15/28 = 13/28.
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by ketkoag » Thu May 07, 2009 11:07 am
i solved the question with the second way and i got the same answer that is : 13/28 . so i think there is misprint in the answer choices coz the choice is 13/26. right??
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