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Four integers are randomly selected from the set {-1,0,1}, with

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Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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New post Updated on: 23 Apr 2017, 02:57
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Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81

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Originally posted by VyshakhR1995 on 23 Apr 2017, 00:20.
Last edited by Bunuel on 23 Apr 2017, 02:57, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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New post 23 Apr 2017, 03:36
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The total probability is selecting any of the 3 integers in the 4 turns= 3*3*3*3= 81

Minimum Product (Least Value) = -1

Case 1: Selecting three "-1" and one "1"
=4!/3!=4

Case 2:Selecting three "1" and one "-1"
=4!/3!=4

Required Probability= (4+4)/81= 8/81
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Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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New post 30 Apr 2017, 07:39
Minimum Product of four items on the list = -1
Number of ways to achieve the result= 2 {(3 Nos -1 + 1 Nos 1) OR (3 Nos +1 + 1 Nos -1)}

Probability for case 1 (3 Nos -1 + 1 Nos 1)
Number of ways= 4 (+1,+1,+1,-1/+1,+1,-1,+1/.........)
Probability = 4x (1/3)^4 = 4/81

Probability for case 2 (3 Nos +1 + 1 Nos -1)
Number of ways= 4 Similar explanations as earlier
Probability = 4x (1/3)^4= 4/81

Hence total probability= 4/81 +4/81= 8/81
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Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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New post 30 Apr 2017, 11:15
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VyshakhR1995 wrote:
Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81


Solution



    • We have a negative number in the set, so the least value will be possible, only when the product is negative.

    • If the product is least and negative, we cannot select 0, so we need to select a combination of -1 and 1 to get a product of -1.

    • Since 4 numbers are selected –

      o We get a product of -1 if we select one -1 and three 1s.

         We can do that in 4C3 ways = 4 ways

      o OR we can select three -1s and one 1.

         We can do that same in 4C3 = 4 ways.

    • Thus, the total ways to get a least value \(= 4 + 4 = 8\) ways

    • Now total ways of selecting a number \(= 3*3*3*3 = 81\)

      o Thus, the probability of choosing the 4 integers whose product has least value \(= \frac{8}{81}\)

    • Hence, the correct answer is Option C.


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Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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New post 30 Jun 2017, 04:28
EgmatQuantExpert wrote:
VyshakhR1995 wrote:
Four integers are randomly selected from the set {-1,0,1},with repetitions allowed.What is the probability that the product of the four integers chosen will be its least value possible

A. 1/81
B. 4/81
C. 8/81
D. 10/81
E. 16/81


Solution



    • We have a negative number in the set, so the least value will be possible, only when the product is negative.

    • If the product is least and negative, we cannot select 0, so we need to select a combination of -1 and 1 to get a product of -1.

    • Since 4 numbers are selected –

      o We get a product of -1 if we select one -1 and three 1s.

         We can do that in 4C3 ways = 4 ways

      o OR we can select three -1s and one 1.

         We can do that same in 4C3 = 4 ways.

    • Thus, the total ways to get a least value \(= 4 + 4 = 8\) ways

    • Now total ways of selecting a number \(= 3*3*3*3 = 81\)

      o Thus, the probability of choosing the 4 integers whose product has least value \(= \frac{8}{81}\)

    • Hence, the correct answer is Option C.


Thanks,
Saquib
Quant Expert
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Thank you for your explanation, e-GMAT expert.

Btw I have a general question, hope that you will help me clear this concern:
How can we know whether order of selection matters in a probability question? In other words, what are the indicators of order of selection?

In the above question, initially I didn't consider the order of 4 numbers chosen, so I worked out an answer different from all 5 choices. But then I realized the denominator is very big, I thought I might overlook many cases... the selecting order could be the key... so I calculated again and figured out the correct answer.

Since the above question is not an official one, I cannot draw any conclusion as to whether there is any OG/GMATPrep question in which no indicator is provided, and we have to test each case. I believe that such an experience expert as you could give me a reliable answer.

Thank you in advance.
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Re: Four integers are randomly selected from the set {-1,0,1}, with  [#permalink]

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Re: Four integers are randomly selected from the set {-1,0,1}, with   [#permalink] 15 Oct 2018, 15:38
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