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# A jar contains 16 red balls and 8 white balls. If 3 balls are selected

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

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29 Aug 2018, 23:53
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:55) correct 33% (01:59) wrong based on 108 sessions

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[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 09 Apr 2017 Posts: 25 Location: Nepal Concentration: Finance, Entrepreneurship WE: Information Technology (Computer Software) A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags 30 Aug 2018, 00:12 MathRevolution wrote: [Math Revolution GMAT math practice question] A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white? A. 0.02 B. 0.03 C. 0.04 D. 0.05 E. 0.06 3 balls selected without replacement. P(WWW) = 8/24 * 7/23 *6/22 = 7/253 = 0.027 Senior Manager Joined: 04 Aug 2010 Posts: 351 Schools: Dartmouth College Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags 30 Aug 2018, 02:21 MathRevolution wrote: [Math Revolution GMAT math practice question] A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white? A. 0.02 B. 0.03 C. 0.04 D. 0.05 E. 0.06 P(1st marble is white) = $$\frac{8}{24}$$ (Of the 24 marbles, 8 are white.) P(2nd marble is white) = $$\frac{7}{23}$$ (Of the 23 remaining marbles, 7 are white.) P(3rd marble is white) = $$\frac{6}{22}$$ (Of the 22 remaining marbles, 6 are white.) To combine these probabilities, we multiply: $$\frac{8}{24} * \frac{7}{23} * \frac{6}{22} = \frac{1}{3} * \frac{7}{23} * \frac{3}{11} = \frac{7}{23*11} = \frac{7}{253} ≈ \frac{7}{250} = \frac{28}{1000} = 0.028 ≈ 0.03$$ _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 759 A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags 30 Aug 2018, 03:25 MathRevolution wrote: [Math Revolution GMAT math practice question] A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white? A. 0.02 B. 0.03 C. 0.04 D. 0.05 E. 0.06 $${\text{Jar}}\,\,\left\{ \begin{gathered} 16\,r \hfill \\ 8\,w \hfill \\ \end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,3\,\,{\text{simultaneous}}\,\,{\text{extractions}}$$ $${\text{? = P}}\left( {{\text{all}}\,\,w} \right)$$ $${\text{total}} = C\left( {16 + 8,3} \right) = C\left( {24,3} \right)\,\,\,\,{\text{equiprobable}}$$ $${\text{favorable}} = C\left( {8,3} \right)$$ $$? = \frac{{C\left( {8,3} \right)}}{{C\left( {24,3} \right)}} = \cdots = \frac{7}{{253}}$$ $${\left( ? \right)^{ - 1}} = \frac{{210 + 42 + 1}}{7} = \boxed{36\frac{1}{7}}$$ $${\left( A \right)^{ - 1}} = {\left( {\frac{2}{{100}}} \right)^{ - 1}} = 50$$ $${\left( B \right)^{ - 1}} = {\left( {\frac{3}{{100}}} \right)^{ - 1}} = \frac{{99 + 1}}{3} = \boxed{33\frac{1}{3}}$$ From the fact that 33 1/3 is less than 36 1/7 , we are sure the other alternative choices (all of them are in increasing order) are not closer to our FOCUS. (In other words, the reciprocals of (C), (D) and (E) are certainly less than 33 1/3 , hence the closest to 36 1/7 is 33 1/3.) The above follows the notations and rationale taught in the GMATH method. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net CEO Joined: 11 Sep 2015 Posts: 3440 Location: Canada A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags Updated on: 30 Aug 2018, 09:35 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white? A. 0.02 B. 0.03 C. 0.04 D. 0.05 E. 0.06 There are 24 balls in the jar (before any are removed) P(all 3 balls are white) = P(1st ball is white AND 2nd ball is white AND 3rd ball is white) = P(1st ball is white) x P(2nd ball is white) x P(3rd ball is white) = 8/24 x 7/23 x 6/22 = 1/3 x 7/23 x 3/11 = 7/253 ASIDE: rather than perform long division, we can take 7/253 and create an equivalent fraction by multiplying top and bottom by 4 to get... 7/253 = (7)(4)/(253)(4) ≈ 28/1000 ≈ 0.028 ≈ 0.03 Aside: I'm not suggesting that it would be wrong to use long division to convert 7/253 to a decimal. That's a perfectly valid approach. However, if you're looking for an alternative approach, then we can also apply the above approach. Answer: B RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Originally posted by GMATPrepNow on 30 Aug 2018, 06:47. Last edited by GMATPrepNow on 30 Aug 2018, 09:35, edited 1 time in total. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 759 Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags 30 Aug 2018, 07:31 GMATPrepNow wrote: ASIDE: rather than perform long division, we can take 7/253 and create an equivalent fraction by multiplying top and bottom by 4 to get... 7/253 = (7)(4)/(253)(4) ≈ 28/1000 ≈ 0.028 ≈ 0.03 Long division is something that must be avoided. That´s why GMATH´s approach deals with what we call "breaking numbers". It is not comfortable to do (say) 253/7 by long division - and we did not - this can be done WITHOUT APPROXIMATIONS easily, as we did and the way we repeat below: 253 = 210 + 42 + 1 , this choice is "smart" because 210 and 42 are not only divisible by 7 (obviously), but also because their quotients are trivial (30 and 6)... Therefore 253/7 = 210/7 + 42/7 + 1/7 = 36 + 1/7 , without FULL PRECISION! One last detail: When we approximate (say) 7/253 by 7/250 , we must be cautious because approximations in denominators may have "small errors" that propagate according to the "magnitude" (absolute value) of the numerator... that´s why we believe the approach we have taken is safer, although in this case the approximation 7/253 by 7/250 was sufficiently good for the alternative choices purposes. The above follows the notations and rationale taught in the GMATH method. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6967 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected [#permalink] ### Show Tags 02 Sep 2018, 17:50 => There are 24C3 ways of choosing $$3$$ balls from the $$24$$ in the jar, and 8C3 ways of choosing $$3$$ balls from the $$8$$ white balls. Therefore, the probability of choosing $$3$$ white balls from the jar is: 8C3 / 24C3 = $${ (\frac{8*7*6)}{(1*2*3)} } / {\frac{(24*23*22)}{(1*2*3)} } = \frac{(8*7*6)}{(24*23*22)} = \frac{7}{( 23* 11 )} ≒ \frac{1}{(3*11)} ≒ 0.03$$ Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 02 Aug 2009
Posts: 7334
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

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02 Sep 2018, 19:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06

Now picking up three balls in 24 balls is a very basic question in GMAT and is equal to $$\frac{8C3}{24C3}$$..
This as shown above equals $$\frac{8*7*6}{24*23*22}$$=$$\frac{7}{253}$$..
Of course the biggest question is how do you simplify 7/253..
All methods shown above are correct..

1) 7/253 can be easily written as 7*4/250*4=28/1000=0.028 As also shown by GMATPrepNow
A decrease of 3 in 253 is perfectly fine . Of course don't decrease by 3 if the denominator is small, say make 13 as 10 in denominator as it will have a huge effect.

2) you can get the denominator to slightly friendly terms when compared to numerator 7.
253 lies between 210 and 280, so answer should be between 7/210 and 7/280.
7/210=1/30=0.033 and 7/280=1/40=0.025
So all values between 210 and 280 will be approximated to 0.03

You have to look at the way that suits you and can vary from person to person
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Affiliations: Target Test Prep
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Posts: 2827
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

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04 Sep 2018, 03:49
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06

The probability of selecting 3 white balls is:

8/24 x 7/23 x 6/22 = 1/3 x 7/23 x 3/11 = 7/23 x 1/11 = 7/253 = 0.0277 ≈ 0.03

Alternate Solution:

The total number of ways that we can draw 3 balls from 24 balls is 24C3 = 24!/(3! x 21!) = 24 x 23 x 22 / 3 x 2 x 1 = 8 x 23 x 11 = 2024.

The number of ways we can pick 3 white balls out of 8 white balls is 8C3 = 8!/(3! x 5!) = 8 x 7 x 6 / 3 x 2 x 1 = 4 x 7 x 2 = 56. The total number of ways we can pick 0 red balls out of 16 red balls is 1.

Thus, the number of ways to pick 3 white balls out of 3 picks, when there are 8 white balls and 16 red balls is by getting 3 white balls and no red balls, out of a total of 24 balls to choose from: (8C3 x 16C0) / 24C3 = 56 x 1 / 2024 = 0.0277 ≈ 0.03

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Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected   [#permalink] 04 Sep 2018, 03:49
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