The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
0 votes
In the cartesian plane, selection of a point P along the y axis in [0,2] is uniformly random. Similarly selection of a point Q along the x axis in [0,2] also uniformly distributed. What is the probability of the area of the triangle POQ to be less than or equal to 1, where O is the origin ?
asked in Probability by Veteran (57.5k points) | 272 views
i found 0.846. Please verify.
I am getting 0.5
upload image,how you did it.

1 Answer

0 votes

Area of POQ=$\frac{1}{2}*2*2=2$

Area less than or equal to 1 is $\frac{1}{2}*1*2=1$

So, Probability of POQ less than equal to 1 is $\frac{1}{2}=0.5$

answered by Veteran (70.4k points)

You have not considered the part x = [1,2] where y can be in range [0,$\frac{2}{x}$]


we need $\frac{xy}{2} \leq 1$ Or, $xy \leq 2$

Just take the area under this rectangular hyperbola bounded by four lines:


Required area = $\frac{1+\ln (2)}{2}$

=>P = 0.846


We can do by the integration method in two parts

  • first, x from zero to 1 => p = 0.5 [ valid y range here is [0,2] ]
  • second , x from 1 to 2 => p = 0.346 [ valid y range here is [0,2/x] ]
  • P = 0.846
Can you Please Explain the the Integration part i.e. how you are getting the values?

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

29,138 questions
36,959 answers
34,803 users