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

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Intern
Joined: 23 Sep 2018
Posts: 3
A bag contains 6 balls of one or more colors. A ball is picked and is  [#permalink]

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03 Nov 2018, 22:20
1
00:00

Difficulty:

75% (hard)

Question Stats:

27% (01:03) correct 73% (01:44) wrong based on 26 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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Joined: 22 Feb 2018
Posts: 398
Re: A bag contains 6 balls of one or more colors. A ball is picked and is  [#permalink]

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03 Nov 2018, 22:38
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 &nbs [#permalink] 03 Nov 2018, 22:38
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