1 / 6

Conditional Probability

Conditional Probability. Problem 6.76. We choose points at random in a square with sides 0≤ x ≤1 and 0≤ y ≤1. Since the area of the square is one, we have a density curve, and the probability that the point falls within any region of the square is the area of that region.

stevesutton
Download Presentation

Conditional Probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Conditional Probability Problem 6.76

  2. We choose points at random in a square with sides 0≤x ≤1 and 0≤y ≤1. Since the area of the square is one, we have a density curve, and the probability that the point falls within any region of the square is the area of that region. Let X be the x-coordinate and Y be the y-coordinate of any point chosen.

  3. Our assignment is to find the conditional probability P(Y<1/2|Y>X). After drawing the square, next draw the lines y=1/2 and y=x, as we prepare to graph the inequalities.

  4. Shade the appropriate portions of the square that meet each condition. Shade the area where y<1/2.

  5. Now shade the area where y>x. To find the P(Y<1/2|Y>X) we find the area of intersection divided by the area where the condition y>x is met.

  6. The area of intersection is a triangle with a base of 1/2 and a height of 1/2 so the area=1/8. The area where y>x is 1/2. So, and the probability is 1/4.

More Related