If 2 real numbers between 0 and 10 are randomly chosen, what is the

Question

If 2 real numbers between 0 and 10 are randomly chosen, what is the probability that the distance between them is at most 7?

A. 0.91
B. 0.87
C. 0.85
D. 0.79
E. 0.70

ramlala · Answer

Total possible outcome = 10 x 10 = 100
possible outcome > 7 = 3 x 3 = 9

Probability  <  7 =  \frac{100-9}{100}  =  \frac{91}{100}  = 0.91

IMO A

chetan2u · Answer

Here let the two numbers be x and y. 
As these REAL numbers can be anything, 5.5 and 8 or 9 and 7 or 1.1 and 4.5, and are related to each other, the question is testing area concept and we can draw a square on x-y axis.

The value of x and y can vary from 0 to 10, so we draw a square of 10*10 as shown in the figure attached. This square represents all possible combinations of (x,y).

Now we are looking at maximum distance to be 7 between them.
There will be two such cases
1) When x is 0, y can be anything from 7 to 10, and  as x increases, the range of y also decreases . This can be depicted by a line joining (0,7) to (3,10). The area between these two points and (0,10) will give all such combinations of real numbers, where y>x. 
2) Similarly, the area between (10,0), (7,0) and (10,3) will give the combinations of two real numbers where x>y.

The total area is 10*10=100
Area where the distance is 7 at the most = Total- Area of triangles = 100-2*(\frac{1}{2}*3*3)=100-9=91

Probability of picking numbers or (x,y) in this area =  \frac{91}{100}=0.91

A

Kuanl · Answer

can u plz explain the pairs 
(0,10) (0,9) (0,8) (10,0) (9,0) (8,0) (1,10) (1,9) (10,1) (9,1) (2,10) (10,2) these pairs have distance more than 7

chetan2u · Answer

Also the question talks of real numbers. So it could well be (0.1,9.9), (1.5,9) etc. This is the reason why you have to do it with the concept of area

tgubbay1 · Answer

This is the coolest answer I've ever seen - thank you!

Suruchim12 · Answer

chetan2u  Hi,

can you please explain your method in detail and specifically how, when the question says that the max. distance between x and Y is 7, how can y be values between 7-10 when x=0?

when x=0, y needs to be a value that when subtracted from x gives a max. value of 7 right, but 8,9 or 10 -0 gives a value more that 7.

Thanks!

Urvasi · Answer

HI!, since 0 is not a real number, i get 6 combinations (1,10) (1,9) (10,1) (9,1) (2,10) (10,2) ( which have more than 7 distance) Can anyone share the 9 sets?

ThatDudeKnows · Answer

Urvasi

Fractions are also real numbers, so you need to account for non-integers, too. The solution posted by  chetan2u  is one of the best for any question anywhere on the forum; check it out!!

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If 2 real numbers between 0 and 10 are randomly chosen, what is the

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