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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:

60% (01:44) correct 40% (01:36) wrong based on 69 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 $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" 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: 7672 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 _________________ Manager Joined: 08 Sep 2016 Posts: 113 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: 6152 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 Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7349 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$149 for 3 month Online Course"
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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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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 $$\frac{1}{2}$$

Therefore, C is the answer.
Answer: C

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
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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 $$\frac{1}{2}$$

Therefore, C is the answer.
Answer: C

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
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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

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