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

• 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.
• 9 years agoHelpfull: Yes(13) No(7)
• Can you(Ayan) explain how the no of ways not to get a triangle of 3 dots=15 ?
• 9 years agoHelpfull: Yes(8) No(0)
• hiii ...friends in this website how can we know this as correct ans?
• 9 years agoHelpfull: Yes(3) No(0)
• 412/455 i think is d answer....
  
• 9 years agoHelpfull: Yes(1) No(0)
• 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 .
• 9 years agoHelpfull: Yes(0) No(0)