HELP geometric probability: area of a square and conditional probability

In summary: You could solve this equation for the area, but it's easier to calculate the conditional probability. P(y<1/2| y> x) is .5, so the area of the triangle is .25. This triangle only covers a 25% of the square.
  • #1
SusanCher89
2
0

Homework Statement



Chose a point at random in a square with sides 0<x<1 and 0<y<1. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability P(y<1/2 / y>x).

Homework Equations



No clue.

The Attempt at a Solution



Apparently, according to the prof, the square need not be equilateral? And this is where I get stumped.

No clue here. Any help would be great.
 
Physics news on Phys.org
  • #2
Try drawing a diagram of your square. BTW, a square is equlateral, so I don't know what your prof was talking about, or maybe you misunderstood him/her.

P(y < 1/2 | y > x) asks for the probability that a point's y coordinate is less than 1/2, given that the point is in the triangular region above and to the left of the line y = x. There is some geometry here that you can use.
 
  • #3
Thanks for your answer, Mark 44.

Let's assume that a square has equilateral sides (which it does, usually). That means that y=x! So P(y>x)= 0 Right!

Also, P(y<1/2) = .5, right??

I'm still pretty lost, any help is appreciated!

:)
Dania
 
  • #4
the sides of the square are given (and by definition equal), so i don't really understand teh equilateral discussion...

anyway, the area of the square is 1
the probability of a point being in the square is 1

you shouldn't have to work too hard to convince yourself, that the probabilty of finding the point in a given region is in fact equal to the area of the region in this case

use that fact with the conditional probability equation to solve
 
  • #5
SusanCher89 said:
Thanks for your answer, Mark 44.

Let's assume that a square has equilateral sides (which it does, usually).
Not "usually"- "always"

That means that y=x! So P(y>x)= 0 Right!
No, not right! (x, y) are coordinates of some point in the square, not the lengths of the sides.

Also, P(y<1/2) = .5, right??
If all points in the square are equally likely, yes. But you want the probability that y< 1/2 given that y> x so P(y< 1/2| y> x) is not necessarily 1/2.

[/quote]I'm still pretty lost, any help is appreciated!

:)
Dania[/QUOTE]
Draw a picture. To start with, of course, draw the square [itex]0\le x\le 1[/itex], [itex]0\le y\le 1[/itex]. Now draw the line y= x. That will be a diagonal of the square. Requiring that y> x means we are in the upper half of that square, above the diagonal. Draw the line y= 1/2. Saying that y< 1/2 means we are below that line but still in the upper half of the square, above the diagonal. You should see that this area is a triangle. What is the area of that triangle? What percentage is it of the upper half of the square?
 

What is geometric probability?

Geometric probability is a branch of mathematics that deals with the calculation of the likelihood of an event occurring in a geometric setting, such as determining the area of a shape or the probability of a point falling within a specific region.

How do you calculate the area of a square?

The formula for finding the area of a square is side length squared, or A = s^2. This means that you multiply the length of one side of the square by itself to find the total area.

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is represented by P(A|B), where A is the event of interest and B is the known event that has occurred.

How do you use conditional probability to calculate geometric probability?

In geometric probability, conditional probability is used to calculate the likelihood of a point falling within a specific region within a shape. This can be done by dividing the area of the desired region by the total area of the shape.

Can geometric probability be applied to real-life situations?

Yes, geometric probability can be used in many real-life situations, such as predicting the likelihood of a dart landing in a specific area on a dartboard or determining the probability of a meteor landing in a certain location on Earth.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
4
Views
416
  • Precalculus Mathematics Homework Help
Replies
14
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
10
Views
1K
  • Precalculus Mathematics Homework Help
Replies
20
Views
2K
  • Precalculus Mathematics Homework Help
Replies
29
Views
1K
  • Precalculus Mathematics Homework Help
Replies
12
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
2K
  • Precalculus Mathematics Homework Help
Replies
12
Views
2K
Back
Top