document.write( "Question 221752: an urn contains 4 red, 2 white, and 4 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue? \n" ); document.write( "

Algebra.Com's Answer #166242 by jsmallt9(3758) $\"\"$ $\"About$

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The direct, straightforward way to solve this is to find the probability of exactly 1 blue marble, exactly 2 blue marbles and exactly 3 blue marbles and then add these probabilities together for your answer. This is not easy.

\n" ); document.write( "It is easier to realize that the probability of at least one blue marble is (1 - probability of zero blue marbles)! So all we need to figure out is the probability of zero blue marbles.

\n" ); document.write( "With the first selection the probability of not selecting a blue marble: 6/10 = 3/5.
\n" ); document.write( "With the second selection the probability of not selecting a blue marble (given that no blue marble has been selected earlier): 5/9.
\n" ); document.write( "With the third selection the probability of not selecting a blue marble (given that no blue marble has been selected earlier): 4/8 = 1/2.
\n" ); document.write( "The probability of all three:
\n" ); document.write( " $\"%283%2F5%29%285%2F9%29%281%2F2%29+=+1%2F6\"$
\n" ); document.write( "So the probability of picking at least one blue = 1 - 1/6 = 5/6. \n" ); document.write( "

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