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# What is the probability of picking a blue ball in 2nd pick from a bag

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Math Expert
Joined: 02 Aug 2009
Posts: 7960
What is the probability of picking a blue ball in 2nd pick from a bag  [#permalink]

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13 May 2016, 03:43
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3
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Difficulty:

55% (hard)

Question Stats:

54% (01:16) correct 46% (01:18) wrong based on 154 sessions

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What is the probability of picking a blue ball in 2nd pick from a bag containing only blue and red ball, if the first ball picked was red?

(1) the number of red ball is one more than the number of blue ball.
(2) the number of red ball is 7.

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Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1686
Location: India
Re: What is the probability of picking a blue ball in 2nd pick from a bag  [#permalink]

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13 May 2016, 04:22
2
Let 'b' be the number of blue balls
Let 'r' be the number of red balls

Total number of balls = r + b

1 red ball is picked --> Number of balls left = r + b - 1

Probability of picking a blue ball from the remaining balls = b/(r + b - 1)

St1: the number of red ball is one more than the number of blue ball. --> r - b = 1 --> r = b + 1
Probability = b/(r + b - 1) = b/(b + 1 + b - 1) = 1/2
Sufficient

St2: the number of red ball is 7 --> Probability = b/(b + 6) --> Not Sufficient

Retired Moderator
Joined: 22 Aug 2013
Posts: 1430
Location: India
Re: What is the probability of picking a blue ball in 2nd pick from a bag  [#permalink]

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25 Jan 2018, 22:52
2
chetan2u wrote:
What is the probability of picking a blue ball in 2nd pick from a bag containing only blue and red ball, if the first ball picked was red?
(1) the number of red ball is one more than the number of blue ball.
(2) the number of red ball is 7.

(1) Well number of red balls = number of blue balls + 1, and we are given that the first ball picked is red.
As soon as a red ball is picked, it makes number of blue and red balls equal. So no matter the total number of balls (or of any color), now we at least know that half the balls are red and half the balls are blue. So probability of picking blue ball in second pick = that of red ball = 1/2.
Sufficient.

(2) So there are 7 red balls, and the first ball picked is also red. This leaves 6 red balls in the bag, but without knowing the number of blue balls or the ratio of blue to red balls, we cannot find the probability of picking a blue ball in second pick. Not Sufficient.

Intern
Joined: 18 Mar 2017
Posts: 1
Re: What is the probability of picking a blue ball in 2nd pick from a bag  [#permalink]

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17 Dec 2018, 15:43
1
What about the case when we have just 1 red ball in the bag?
Intern
Joined: 12 Nov 2017
Posts: 1
Re: What is the probability of picking a blue ball in 2nd pick from a bag  [#permalink]

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18 Dec 2018, 07:49
what if repetetion is allowed?
Re: What is the probability of picking a blue ball in 2nd pick from a bag   [#permalink] 18 Dec 2018, 07:49
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# What is the probability of picking a blue ball in 2nd pick from a bag

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