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

Question

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

Tan2017 · Answer

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

Shubhranil88 · Answer

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

EgmatQuantExpert · Answer

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 e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

Lucy Phuong · Answer

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.

TexasANA · Answer

guys, ssory for the stupid question, but i do not get how the total ways of selecting number is 81?

Fdambro294 · Answer

I didn’t follow the combinations approach. I used Probability of independent events and the binomial theorem.

The minimum value we can get as a Product of 4 values picked from the given Set is ———> (-1)

Given that we are pulling 4 numbers with NO REPLACEMENT - we can accomplish this in 2 ways

Scenario 1:

Pull -1
Pull -1
Pull -1
Pull +1

OR

Scenario 2:

Pull -1
Pull +1
Pull +1
Pull +1

Call the prob of pulling -1 ——-> P(A) = 1/3

Call the prob of pulling +1 ———> P(B) = 1/3

Scenario 1:
A - A - A - B

The different ways this event can occur is given by: 4!/3! = 4 ways

AND

P(A) * P(A) * P(A) * P(B) = (1/3) (1/3) (1/3) (1/3) = 1/81

Probability that scenario 1 occurs = (4) (1/81) = 4/81

OR

Scenario 2:

A - B - B - B

The logic will be the same, as well as the calculation

(4!/3!) * (1 / 3^4) = 4/81

Probability of getting a Product of (-1) from 4 picks from the set with No Replacement is equal to:

(4/81) + (4/81) =

8/81

Posted from my mobile device

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