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A bag contains 6 balls of one or more colors. A ball is picked and is

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Joined: 23 Sep 2018
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A bag contains 6 balls of one or more colors. A ball is picked and is  [#permalink]

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New post 03 Nov 2018, 23:20
1
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

22% (01:22) correct 78% (01:50) wrong based on 31 sessions

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A bag contains 6 balls of one or more colors. A ball is picked and is found to be red. What's the probability that the bag initially had exactly 6 red balls?

A. 2/7
B. 1/5
C. 3/5
D. 4/5
E. 1/7


This question tests the concept of conditional probability and I really found the solution mind-boggling. It would be great if one of the experts could provide a more comprehensive solution to such problems. The source is not official GMAT but it is a great question from one of the CAT forums and I thought it checks all boxes of a supremely tough 700+ question. This is my first question post and although I did go through the rules of posting twice, I apologise in advance for any discrepancy or bug. Kindly help- Bunuel VeritasKarishma :)
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Re: A bag contains 6 balls of one or more colors. A ball is picked and is  [#permalink]

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New post 03 Nov 2018, 23:38
3
1
OA: A

probability of drawing 1 red ball, when there is 1 red ball out of 6 total balls \(= \frac{1}{6}\)
probability of drawing 1 red ball, when there are 2 red ball out of 6 total balls\(=\frac{2}{6}\)
probability of drawing 1 red ball, when there are 3 red ball out of 6 total balls\(=\frac{3}{6}\)
probability of drawing 1 red ball, when there are 4 red ball out of 6 total balls\(=\frac{4}{6}\)
probability of drawing 1 red ball, when there are 5 red ball out of 6 total balls\(=\frac{5}{6}\)
probability of drawing 1 red ball, when there are 6 red ball out of 6 total balls\(=\frac{6}{6}\)

probability that there are all 6 reds ball,given that we know 1 drawn ball is red ball \(= \frac{\frac{6}{6}}{\frac{1}{6}+\frac{2}{6}+\frac{3}{6}+\frac{4}{6}+\frac{5}{6}+\frac{6}{6}}=\frac{2}{7}\)
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Re: A bag contains 6 balls of one or more colors. A ball is picked and is   [#permalink] 03 Nov 2018, 23:38
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A bag contains 6 balls of one or more colors. A ball is picked and is

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