Question 221752
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.<br>
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.<br>
With the first selection the probability of not selecting a blue marble: 6/10 = 3/5.
With the second selection the probability of not selecting a blue marble (given that no blue marble has been selected earlier): 5/9.
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.
The probability of all three:
{{{(3/5)(5/9)(1/2) = 1/6}}}
So the probability of picking at least one blue = 1 - 1/6 = 5/6.