If a number between 0 and 1/2 is selected at random, which

Question

If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A. 0 and 3/20
B. 3/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2

KarishmaB · Accepted Answer

The question is one of probability. You select a number between 0 and 1/2 at random. 
The number is between 0 and 10/20 (for ease of calculations)

Now, wider the desired range of the options, more is the probability that the number will lie in that range. 
The probability that the number will lie between 0 and 10/20 is 1 i.e. the number is in this range. The probability that the number will lie between 0 and 9/20 is a little less than 1 since it is quite possible that the number is in this range but there is a small chance that it lies between 9/20 and 10/20 which this range doesn't cover. The probability that the number will lie between 0 and 1/20 is very small since this range covers a small part of the total range.
 
A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.

Answer (E)

BrentGMATPrepNow · Answer

We need to determine the LENGTH OF EACH INTERVAL.

The interval that has the greatest length, will be the most likely interval.

To determine the length of each interval, it may be faster to first  convert the fractions to decimals . We get:

A) 0 and 0.15  (interval length = 0.15) 
B) 0.15 and 0.2  (interval length = 0.05)  
C) 0.2 and 0.25  (interval length = 0.05) 
D) 0.25 and 0.3  (interval length = 0.05) 
E) 0.3 and 0.5  (interval length = 0.2)

Answer: E

Cheers,
Brent

scthakur · Answer

A. 0 and 3/20 - here difference is 0.15
B. 3/20 and 1/5 - here difference is 0.05
C. 1/5 and 1/4 - here difference is 0.05
D. 1/4 and 3/10 - here difference is 0.05
E. 3/10 and 1/2 - here difference is 0.2

Hence, E.

GMAT TIGER · Answer

Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.

Now you have excellent explanantion by  scthakur . In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it.

AkshayDavid · Answer

Can you please explain why did you eliminate first four choices?
as per my understanding 0 and 1/2 include these numbers also --> 0.15, 0.05, 0.05, 0.05 
please correct me if i am missing something

Bunuel · Answer

Similar questions to practice: if-a-number-between-0-and-1-is-selected-at-random-which-of-130819.html if-a-number-between-1-and-1-2-is-selected-at-random-which-of-101786.html

mayank3003 · Answer

Best way (perhaps) is to make all the answers in the "../20" fraction-format. Computing intervals will become easier. We avoid computing decimal values through this way

GmatPrime · Answer

Another way is to plot the numbers on the number line.

Attachment:

File comment: Number line:

fullsizeoutput_5f3.jpeg [ 984.64 KiB | Viewed 29805 times ]

Option E has the greatest difference, i.e. 0.20.
Hence, the probability would be maximum for this option, since the range is maximum.

CEdward · Answer

In simplest terms, the question is asking us which of the following ranges is the largest. 
The answer is E: 0.3 - 0.5 has a range of 0.20 (0.5 - 0.3).

If you really want to connect that to probability, what I just did above is the numerator. The denominator is the difference between 0 and 0.5 (0.5 - 0 = 0.5)

So the probability is 2/5 / 1/2 = 4/5 = 0.80 ---> 0.80 x 100 = 80% probability that it lands in that range.

E.

Hoji · Answer

I made the denominator 60 so:
A) 0/60 - 9/60
B) 9/60 - 12/60
C) 12/60 - 15/60
D) 15/60 - 20/60
E) 20/60 - 30/60

option E has the greatest range thus the greatest probability that the selected number falls into this range

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