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Jean drew a gumball at random from a jar of pink and blue

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iwillcrackgmat
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Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   Updated on: 19 Mar 2012, 03:16
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Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?

A. 1/49
B. 4/7
C. 3/7
D. 16/49
E. 40/49
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B

Originally posted by iwillcrackgmat on 19 Mar 2012, 02:32.
Last edited by Bunuel on 19 Mar 2012, 03:16, edited 1 time in total.
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Re: Jean drew a gumball at random from a jar of pink and blue gu [#permalink] New post   19 Mar 2012, 02:45
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The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 9/49 = (3/7) * (3/7)

Therefore probability that the next one she draws is pink = 4/7

Option (B)
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Re: Jean drew a gumball at random from a jar of pink and blue gu [#permalink] New post   19 Mar 2012, 03:13
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iwillcrackgmat wrote:
Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?

A. 1/49
B. 4/7
C. 3/7
D. 16/49
E. 40/49


The probability of picking a blue gum is \(\frac{blue}{total}\), the probability of picking two blue gums in a row (with replacement) is \(\frac{blue}{total}*\frac{blue}{total}\) --> \(\frac{blue}{total}*\frac{blue}{total}=\frac{9}{49}\) --> \(\frac{blue}{total}=\frac{3}{7}\).

Since there are ONLY pink and blue gums in the jar then the probability of picking pink would be \(1-\frac{3}{7}=\frac{4}{7}\).

Answer: B.
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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   19 Mar 2012, 09:15
thanks for the question.
It appeared like a tough one.
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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   19 Mar 2012, 09:20
These are the questions which generally confuse us with their wordiness..
Welcome to gmat :D
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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   24 Sep 2019, 15:42
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iwillcrackgmat wrote:
Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?

A. 1/49
B. 4/7
C. 3/7
D. 16/49
E. 40/49


Let the probability of drawing a blue gumball be p. Then the probability of drawing two blue gumballs with replacement is 9/49, which means that p^2 = 9/49. Therefore, we have p = √(9/49) = 3/7.

Since the probability of drawing a pink gumball is (1 - p), the probability of drawing a pink gumball is 1 - 3/7 = 4/7.

Answer: B
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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   24 Sep 2019, 18:42
iwillcrackgmat wrote:
Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?

A. 1/49
B. 4/7
C. 3/7
D. 16/49
E. 40/49


Probability of picking a blue gum ball = 3/7*3/7=9/49

Probability of picking a pink gumball = 4/7

IMO B

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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink] New post   07 Feb 2023, 11:18
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Re: Jean drew a gumball at random from a jar of pink and blue [#permalink]
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