probability DS.

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Thu Jan 27, 2011 3:07 am

Q1:If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

1. There are twice as many white balls as black balls in the bowl
2. If two balls are extracted from the bowl, the probability that both of them will be black is 0.

Q2: A bag contains only white and black ball in the ratio of 2:1 resp.. What is the probability of drawing a white ball form the bag.

is there any difference between Q1. part 1 and Q2.??

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 27, 2011 3:07 am

pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pmFollowed by: 5 members; Location: Kolkata, India; Thanked: 11 times

by pesfunk » Thu Jan 27, 2011 3:30 am

Q1 -

Option 1 gives the ratio to find the probability. Sufficient.
Option 2 says that there is only 1 black ball. But we do not know how many white balls are there.

Hence A

advita wrote:Q1:If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

1. There are twice as many white balls as black balls in the bowl
2. If two balls are extracted from the bowl, the probability that both of them will be black is 0.

Q2: A bag contains only white and black ball in the ratio of 2:1 resp.. What is the probability of drawing a white ball form the bag.

is there any difference between Q1. part 1 and Q2.??

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jan 27, 2011 3:48 am

advita wrote:is there any difference between Q1. part 1 and Q2.??

No, they are same.

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pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pmFollowed by: 5 members; Location: Kolkata, India; Thanked: 11 times

by pesfunk » Thu Jan 27, 2011 3:49 am

Is my answer correct ?

Anurag@Gurome wrote:
advita wrote:is there any difference between Q1. part 1 and Q2.??
No, they are same.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jan 27, 2011 3:51 am

pesfunk wrote:Is my answer correct ?

Yes.

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Thu Jan 27, 2011 4:08 am

thanks anurag. ..thanks mate.

here OA is A..!!!

but my doubt:
is it possible to know the probability by knowing ratio only..??

okay... another twist in Q.

Q3: say W:B =4:3 ( that means balls are in the ratio of 4:3.)
what is the probability of drawing a white ball. ??

solution: W:B=4:3 or 8:6 ... so, probability = 4/7 or 8/14(=4/7) ...yeah equal values...fine.

Q4: if i say what is probability of drawing two white balls at random from the bag containing White to black balls in the ration of 4:3. ??

solution: if we take 4:3 then, P=4/7*3/6=2/7
if we take 8:6, p= 8/14*7/13= 4/13..... something different from earlier value.

so, does that means ... in Q1- probability for only one white ball was asked to find out...that is the reason it works.

i hope Q4's solution and reasoning is right.
pl confirm... thanks.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jan 27, 2011 4:16 am

[quote="advita"if i say what is probability of drawing two white balls at random from the bag containing White to black balls in the ration of 4:3. ??

solution: if we take 4:3 then, P=4/7*3/6=2/7
if we take 8:6, p= 8/14*7/13= 4/13..... something different from earlier value.

so, does that means ... in Q1- probability for only one white ball was asked to find out...that is the reason it works.

i hope Q4's solution and reasoning is right.
pl confirm... thanks.[/quote]

Yes, you're correct.
Let me explain a bit.

Say, number of white balls = W and that of black balls = B

P( 1 Black) = B/(B + W) = Ratio of number of black balls to total
P( 1 White) = W/(B + W) = Ratio of number of white balls to total

BUT

P( 2 Black without replacement) = [B/(B + W)]*[(B - 1)/(B + W - 1)] â‰ Ratio of number of black balls to total

Hope it helps.

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