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A certain jar contains only b black marbles, w white marbles [#permalink]

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04 Apr 2007, 16:47

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A certain jar contains only b black marbles, w white marbles and r red marbles. If a marble is picked at random from the jar, is the probability that the marble chosen be red greater than the probability that the marble chosen will be white?
(1) r/(b+w)>w/(b+r)
(2) b-w>r
Answer is A

Probability of choosing red marble = r/(b+w+r)
Probability of choosing white marble = w/(b+w+r)

To compare these two probabilities, we should know the relation between r and w
Lets consider the statement 1:
r/(b+w) > w/(b+r)
r(b+r) > (b+w)w
rb+r^2 -bw_w^2 > 0
b(r-w) + r^2 -w^2 > 0
b(r-w) + (r+w)(r-w) > 0
(r-w)(b+r+w) > 0
as we know b+r+w will always be positive
so r-w> 0
r > w
hence we can say the prob of choosing red marble is greater. SUFF

Statement2 : does not establish any relation between r and w. INSUFF