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A certain jar contains only b black marbles, w white marbles [#permalink]
26 Dec 2007, 19:07

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Difficulty:

35% (medium)

Question Stats:

60% (02:25) correct
40% (01:34) wrong based on 158 sessions

A certain jar contains only b black marbles, w white marbles and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater then the probability that the marble chosen will be white?

Re: DS - Probability [#permalink]
25 Aug 2008, 10:13

jimjohn wrote:

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?

1) r / (b+w) > w / (b+r)

2) b-w > r

1) r / (b+w) > w / (b+r) r(b+r) > w(b+w) ... this is possible only if r>w. suffcieint

2) b-w > r w >r or w<r INSUFFCIENT.

A
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Re: DS - Probability [#permalink]
27 Sep 2009, 10:44

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?

1) r / (b+w) > w / (b+r)

2) b-w > r

Soln. From statements what we need to find is i.e if P(choosing one red) > P(choosing one white) i.e if r / (b+w+r) > w / (b+w+r) or in its simplest form after cancelling out the denominators, if r > w

Statement 1 alone is sufficient. Given that => r / (b+w) > w / (b+r) => (b+r)/w > (b+w)/r adding 1 to both sides and taking common denominator => (b+r+w)/w > (b+w+r)/r cancelling numerators and taking r and w to numerators => r > w

Statement 2 alone is not sufficient Given that => b-w > r from this we cannot find if r > w or r < w Hence not sufficient

Re: DS - Probability [#permalink]
15 Feb 2010, 15:16

jimjohn wrote:

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?

1) r / (b+w) > w / (b+r)

2) b-w > r

Ques: Is r /(b+w+r) > w /(b+w+r) ? or rb + rw + r^2 > wb + w^2 + rw? or rb + r^2 > wb + w^2 ?

S1: r / (b+w) > w / (b+r) rb + r^2 > wb + w^2... Hence SuFF..

S2: b-w>r b > r + w..... this doesnt give r > w or not..... hence INSUFF.

Therefore A.
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Re: DS - Probability [#permalink]
15 Feb 2010, 15:39

jimjohn wrote:

A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?

1) r / (b+w) > w / (b+r)

2) b-w > r

(i) is sufficient because it gives us r<w. Thus we know the answer. From (ii) we can'tsay whether w>r or r>w. Therefore "A"

Re: DS - Probability [#permalink]
17 Feb 2010, 13:53

Damn I'm so bad at DS and inequalities.... scthakur's solution was the easiest for me to understand. Do you guys actually see the answer intuitively without going all the way to the end?