Latest TCS Aptitude Question SOLUTION: 13. Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle? a. 440/455 b. 434/455 c. 449/455 d. 438/455

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13.

Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
a. 440/455
b. 434/455
c. 449/455
d. 438/455

Asked In TCS aspirant (8 years ago)

Unsolved Read Solution (5)

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Read Solution (5) :

Ayan Chowdhury  (8 years ago)

ans: a, total outcome = 15C3= 455.
no.of ways not to get a triangle of 3 dots= 15
probability of getting 3 dots to make a triangle when selected randomly= (455-15)/455= 440/455.

Is this solution Helpfull? Yes (13) | No (7)  

DEBASMITA  (8 years ago)

Can you(Ayan) explain how the no of ways not to get a triangle of 3 dots=15 ?

Is this solution Helpfull? Yes (8) | No   

vamshi krishna  (8 years ago)

hiii ...friends in this website how can we know this as correct ans?

Is this solution Helpfull? Yes (3) | No   

sanghamitra mandal  (8 years ago)

412/455 i think is d answer....

Is this solution Helpfull? Yes (1) | No   

soumya  (8 years ago)

I'm assuming that's three distinct dots. If they don't form a triangle, then they're collinear. Let's enumerate the collinear cases.

They could be three dots in one row (forming a horizontal line). There are (53)=10 ways of selecting three dots from a row, and there are three rows, so that makes 30 cases.

They could be (the) three dots in a column, and there are five columns, so that makes 5 cases.

They could be three dots in positions (1,i),(2,i+1),(3,i+2) , i∈{1,2,3} (thus forming a diagonal of some sort). There are three cases of this kind. But they could also form a diagonal slanted in the opposite direction, so there are three more cases, making a total of 6 cases.

They could be a diagonal of the form (1,1),(2,3),(3,5) , or the one in the opposite direction, so that makes 2 cases.

Thus, there are totally 43 cases. The total number of ways of selecting three dots from the matrix is (153)=455 . Thus, there are 455−43=412 ways of selecting three dots that form a triangle. The probability is, therefore,

412/455 .

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