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Grace has 16 jellybeans in her pocket. She has 8 red ones, 4

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MariaF
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Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   Updated on: 02 Nov 2012, 14:10
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Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16
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Official Answer
D

Originally posted by MariaF on 02 Nov 2012, 12:18.
Last edited by Bunuel on 02 Nov 2012, 14:10, edited 1 time in total.
Renamed the topic and edited the question.
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actleader
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Re: One more easy question [#permalink] New post   02 Nov 2012, 12:56
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MariaF wrote:
ok... My brains don't work for today....
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16


Maria,
I doubt if it is al-gebra.
It is a probability problem.

Grace, in the worst case may take out 8 red jellyes ► 4 green ► and the next will be the blue one.
So 13 - is the minimum number of jellybeans.
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   02 Nov 2012, 14:15
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MariaF wrote:
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16


The worst scenario is when she takes 8 red and 4 green, total of 12 jellybeans, and still doesn't have 3 distinct colors. But the next draw (13th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.

Answer: D.
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   01 Apr 2016, 14:21
The worst case arises when she takes 8 red and 4 green, and still doesn't have 3 distinct colors. So she draws (13th) next which will surely be the third color jellybean (blue) as no other colour jellybean is left in her pocket
Answer - D
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   03 Apr 2016, 07:19
Bunuel wrote:
MariaF wrote:
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16


The worst scenario is when she takes 8 red and 4 green, total of 12 jellybeans, and still doesn't have 3 distinct colors. But the next draw (13th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.

Answer: D.


Shouldn't it be 9 actually...in case she picks G and B, then on 9th trial she can get a R.
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   03 Apr 2016, 11:45
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Avinashs87 wrote:
Bunuel wrote:
MariaF wrote:
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16


The worst scenario is when she takes 8 red and 4 green, total of 12 jellybeans, and still doesn't have 3 distinct colors. But the next draw (13th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.

Answer: D.


Shouldn't it be 9 actually...in case she picks G and B, then on 9th trial she can get a R.


For such cases when we should ensure, guarantee some outcome we always consider the worst case scenario. For 9 picks it's possible that Grace picks 8 R's and 1 G.

Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   04 Aug 2019, 04:56
MariaF wrote:
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

A. 4
B. 8
C. 12
D. 13
E. 16


13 (8+4+1) worst case
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   26 Nov 2020, 14:23
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?

We need to maximize the worst case possibiilty for questions such as this

Total jellybeans = 16
Red =8
Green = 4
Blue = 4

Worst case can be first 8 draws are Red and next 4 are Green, even after 12 draws not all colors are represented. But in the 13th draw, the color has to be Blue. So minimum number of draws required is 13

Ans : 13
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink] New post   12 Aug 2023, 07:01
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Re: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 [#permalink]
12 Aug 2023, 07:01
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