A triangular region has vertices at (1, 2) , (3, 2 ) , and ( 1, 5 ) .

 

Suppose a point ( x, y ) is chosen at random from within the region.

 

What is the probability that x > y ?

I can never figure these things out; but I sure have missed them! :ylsuper:

 

Just for the fun of it, I'll start it off by guessing an obvious answer: 40%

One in seven

I can never figure these things out; but I sure have missed them! :ylsuper:

 

Just for the fun of it, I'll start it off by guessing an obvious answer: 40%

 

 

Birdie, had the vertices been (0,0) , (2, 0) , and (0, 3) , your answer of 40% would have been precisely correct. The vertices given in the teaser make the problem a tad more challenging, but the method is the same.

Birdie, had the vertices been (0,0) , (2, 0) , and (0, 3) , your answer of 40% would have been precisely correct. The vertices given in the teaser make the problem a tad more challenging, but the method is the same.

This is why I never get them right.

 

How about 331/3%?

I'm trying to sketch it out as we speak...

The figure I come up with looks to be about 50% of the size of the triangle.

1 in 12

1 in 3

The probability would be zero.

Here is a graph to help visualize it. (Hope I did this right )

 

The blue line passes through the points (1,1), (2,2), (3,3) etc. This means that every point below the blue line represents where x > y. Amd every point above the blue line represents where x

 

I plotted the triangle using the 3 points of this problem. The yellow area is where x y.

 

.

Here is a graph to help visualize it. (Hope I did this right )

 

The blue line passes through the points (1,1), (2,2), (3,3) etc. This means that every point below the blue line represents where x > y. Amd every point above the blue line represents where x

 

I plotted the triangle using the 3 points of this problem. The yellow area is where x y.

 

.

Dude, I KNOW you don't have that much time on your hands.

 

(I drew my vector straight across the x-axis at y=3)

Dude, I KNOW you don't have that much time on your hands.

 

(I drew my vector straight across the x-axis at y=3)

 

This was more fun than what I have to do. Besides, I'm having my lunch.

Here is a graph to help visualize it. (Hope I did this right )

 

The blue line passes through the points (1,1), (2,2), (3,3) etc. This means that every point below the blue line represents where x > y. Amd every point above the blue line represents where x

 

I plotted the triangle using the 3 points of this problem. The yellow area is where x y.

 

.

 

That's how I see it.....seven points within the triangle (1,2), (1,3), (1,4), (1,5), (2,2), (2,3) and (3, 2 ) and with one point where x>y (3,2)…….. or

 

One in seven (I'm on lunch too! 3 hr time difference though)

That's how I see it.....seven points within the triangle (1,2), (1,3), (1,4), (1,5), (2,2), (2,3) and (3, 2 ) and with one point where x>y (3,2)…….. or

 

One in seven (I'm on lunch too! 3 hr time difference though)

 

 

 

Keep in mind that since we are considering areas, this is a continuous, not a discrete probability distribution. There is an infinity of points both within the big triangle and also the blue triangle(where x>y), not just a countable number as would be the case with a discrete distribution.Thus, x and y are not limited to being integers.