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# A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from

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Math Revolution GMAT Instructor
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A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from  [#permalink]

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Updated on: 18 Apr 2018, 12:14
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Difficulty:

65% (hard)

Question Stats:

62% (01:39) correct 38% (01:30) wrong based on 63 sessions

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[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

$$A. \frac{1}{3}$$
$$B. \frac{3}{8}$$
$$C. \frac{1}{2}$$
$$D. \frac{5}{8}$$
$$E. \frac{3}{4}$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 09 Apr 2018, 02:28. Last edited by Bunuel on 18 Apr 2018, 12:14, edited 3 times in total. Math Expert Joined: 02 Aug 2009 Posts: 6814 Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from [#permalink] ### Show Tags 09 Apr 2018, 08:20 1 MathRevolution wrote: [GMAT math practice question] A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1? $$A. \frac{1}{3}$$ $$B. \frac{3}{4}$$ $$C. \frac{1}{2}$$ $$D. \frac{5}{8}$$ $$E. \frac{3}{8}$$ The choices are not in any order and OA is wrong.. way you can choose first ball - 4 ways Next ball - 4 ways again as ball has been returned.. ways -$$4*4=16$$ ways in which difference is 1.. A) if the first ball is 2 or 3, next ball can be picked in TWO ways 2.... 1 or 3 3..... 2 or 4 so 2*2=4 ways B) but if the first ball is 1 or 4, next ball can be picked in ONE way 1..... only 2 4..... only 3 so 1*2=2 ways total = 2*2+2*1 = 6 Probability = $$\frac{6}{16} = \frac{3}{8}$$.... B _________________ 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 GMAT online Tutor Manager Joined: 08 Sep 2016 Posts: 116 Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from [#permalink] ### Show Tags 09 Apr 2018, 14:48 Total possibilities = 4*4 = 16 Favorable outcomes: If the ball with #1 is chosen = 1 favorable If the ball with #2 is chosen = 2 favorable If the ball with #3 is chosen = 2 favorable If the ball with #4 is chosen = 1 favorable 6/16 = 3/8 answer B Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3527 Location: United States (CA) Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from [#permalink] ### Show Tags 10 Apr 2018, 17:21 MathRevolution wrote: [GMAT math practice question] A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1? $$A. \frac{1}{3}$$ $$B. \frac{3}{8}$$ $$C. \frac{1}{2}$$ $$D. \frac{5}{8}$$ $$E. \frac{3}{4}$$ The following are favorable outcomes for the two draws: 1, 2 2, 1 3, 2 2, 3 3, 4 4, 3 We see that we have 6 favorable outcomes. The total number of outcomes is 4 x 4 = 16, since there are always 4 balls in the jar for each of the two picks. P(that the difference between the numbers on the two balls selected is 1) = 6/16 = 3/8. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6242 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from [#permalink] ### Show Tags 11 Apr 2018, 05:56 => The total number of ways the two balls may be selected is 4C2 =$$\frac{( 4 * 3 )}{( 1 * 2 )} = 6.$$ There are three ways in which the numbers on the two balls selected can have a difference of $$1: ( 1, 2 ), ( 2, 3 )$$, and $$( 3, 4 )$$. Thus, the probability is $$\frac{3}{6}$$ or $$\frac{1}{2}$$ Therefore, C is the answer. Answer: C _________________ 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$99 for 3 month Online Course"
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Math Expert
Joined: 02 Aug 2009
Posts: 6814
Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from  [#permalink]

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11 Apr 2018, 09:33
1
MathRevolution wrote:
=>

The total number of ways the two balls may be selected is 4C2 =$$\frac{( 4 * 3 )}{( 1 * 2 )} = 6.$$
There are three ways in which the numbers on the two balls selected can have a difference of $$1: ( 1, 2 ), ( 2, 3 )$$, and $$( 3, 4 )$$.

Thus, the probability is $$\frac{3}{6}$$ or $$\frac{1}{2}$$

Hi..

you are wrong on two counts..

1) since ball is being returned, ways of picking two balls will be 4*4 and NOT 4C2
2) ways difference is one = (1,2); (2,1) ; (2,3) ; (3,2) ; (3,4); (4,3) so 6 ways
_________________

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

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Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from  [#permalink]

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18 Apr 2018, 00:32
MathRevolution wrote:
=>

The total number of ways the two balls may be selected is 4C2 =$$\frac{( 4 * 3 )}{( 1 * 2 )} = 6.$$
There are three ways in which the numbers on the two balls selected can have a difference of $$1: ( 1, 2 ), ( 2, 3 )$$, and $$( 3, 4 )$$.

Thus, the probability is $$\frac{3}{6}$$ or $$\frac{1}{2}$$

You are wrong.

Total Outcomes : 16
two balls with repetition : 4 * 4 = 16

Favourable Outcomes : 6
4,3 / 3,2 / 2,1 or its inverse that is 3,4 / 2,3 / 1,2

Probability : 6/16 or 3/8
Manager
Joined: 28 Nov 2017
Posts: 145
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Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from  [#permalink]

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18 Apr 2018, 03:23
MathRevolution wrote:
[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

$$A. \frac{1}{3}$$
$$B. \frac{3}{8}$$
$$C. \frac{1}{2}$$
$$D. \frac{5}{8}$$
$$E. \frac{3}{4}$$

Answer is B. Totally agree with the reasoning given by chetan2u
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Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from  [#permalink]

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18 Apr 2018, 04:21
The answer is definitely B because the balls are being replaced.

Total possibilities are 4*4 = 16

The favorable outcomes that fit the question are:
1&2 - 2 ways
2&3 - 2 ways
3&4 - 2 ways

total of 6 favorable outcomes.

6/16 = 3/8

Re: A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from &nbs [#permalink] 18 Apr 2018, 04:21
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# A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from

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