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# In a jar there are balls in different colors: blue, red, green and yel

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In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 18:48
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In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Sep 2014, 14:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 19:30

First step: determine how many balls are in the jar. Essentially, since the number of balls can't be a decimal number, it must be a multiple of 5, 8 and 10. The LCM of those three numbers is 40.

The probability of drawing a blue ball is 1/8. -> 5 blue balls
The probability of drawing a red ball is 1/5. -> 8 red balls
The probability of drawing a green ball is 1/10. -> 4 green balls

Number of yellow balls = 40 - 5 - 8 - 4 = 23
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 19:33
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

a) 23.
b) 20.
c) 24.
d) 17.
e) 25.

The probability of drawing a blue ball is 1/8 = 5/40
The probability of drawing a red ball is 1/5 = 8/40
The probability of drawing a green ball is 1/10 = 4/40
Yellow balls = 40-(5+8+4) = 23

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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 19:49
thanks. This is very helpful. I didnt know how to get that 40.

I am facing challenges with this one too.

In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

a) 4/7
b) 3/7
c) 35/128
d) 4/28
e) 28/135
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 19:59
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Basically you can approach the problem this way:

You choose one specific scenario: R R R R N N N (R = Rain, N = No Rain). The probability for this scenario is (0.5)^7.

You can arrange the R's in 7C4 ways.

$$\frac{1}{2}^7 * 7C4$$

$$= \frac{1}{128} * 35$$

$$= \frac{35}{128}$$

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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 20:12
thanks,

this is really helpful, and explained in a simple way.

Do you know of any online resource that can be of help for probability questions.
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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07 Oct 2009, 20:33
mohana wrote:
thanks,

this is really helpful, and explained in a simple way.

Do you know of any online resource that can be of help for probability questions.

Check this out: http://gmatclub.com/forum/combinations-permutations-and-probability-references-56486.html#p402561
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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08 Oct 2009, 03:36
LCM of (8,5,10) < 50 ....i.e. 40 balls

The probability of drawing a blue ball is Pb = 1/8 : B/40 thus B = 5
The probability of drawing a red ball is Pr = 1/5 : R/40 thus R = 8
The probability of drawing a green ball is Pg = 1/10 : G/40 thus G = 4

Thus Yellow balls = 40-(5+8+4) = 23....OA A
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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08 Oct 2009, 07:24

just add the given probabilities p(blue)+p(red)+p(green) i.e

1/8+1/5+1/10=17/40

now we know p(blue)+p(red)+p(green)+p(yellow)=1

17/40+p(yellow)=1

p(yellow)=23/40

i.e why yellow balls are 23.

if it has been given that that no of balls are more than 50 and less than 100 then it would have been 46.

to select 4 days out of 7=7c4=(7*6*5*4)/(1*2*3*4)=35

now given that there is 50% chance of rain

probability of rain everyday is 1/2

for 7 days=1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128

so probability of rains on 4 out of 7 consecutive days is 35/128

hope this will help
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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03 May 2011, 09:50
total number of balls will have factors 8,5 and 10.Hence the number will be multiple of 40.
total balls = 40
yellow ball = 40- (5+8+4) = 23
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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12 Sep 2014, 13:21
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Re: In a jar there are balls in different colors: blue, red, green and yel [#permalink]

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19 Sep 2014, 23:14
mohana wrote:
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?

A. 23
B. 20
C. 24
D. 17
E. 25

# Blue Balls = Total Balls / 8, similarly #Red Balls = TB/5; #Green Balls = TB/10

# Yellow Balls= TB- #blue-#Red-#Green = (TB*23)/40

SInce y has to be a integer, TB has to be 40. And therefore # Yellow balls =23

ps: i hate questions pertaining to balls.
Re: In a jar there are balls in different colors: blue, red, green and yel   [#permalink] 19 Sep 2014, 23:14
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