1 / 7

CONDITIONAL PROBABILITY

CONDITIONAL PROBABILITY. Consider two events, A and B. Suppose we know that B has occurred. This knowledge may change the probability that A will occur. We denote by P(A|B) the conditional probability of event A given that B has occurred.

duman
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 Consider two events, A and B. Suppose we know that B has occurred. This knowledge may change the probability that A will occur. We denote by P(A|B) the conditional probability of event A given that B has occurred.

  2. To obtain a formula for P(A|B), let us refer to the following figure:

  3. Note that the knowledge that B has occurred effectively reduces the sample space from S to B. Therefore, interpreting probability as the area, P(A|B) is the proportion of the area of B occupied by A:

  4. Example- Tossing Two Dice: Conditional Probability An experiment consists of tossing two fair dice which has a sample space of 6x6=36 outcomes. Consider two events: A={Sum of dice is 4 or 8} and B={Sum of dice is even}

  5. The sum of 4 or 8 can be achieved in eight ways with two dice, so A consists of the following elements: A={(1,3), (2,2), (3,1), (2,6), (3,5), (4,4), (5,3), (6,2)} The sum of the dice is even when both have either even or odd outcomes, so B contains the following pairs: B={(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5), (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6)}

  6. Thus A consists of 8 outcomes, while B consists of 18 outcomes: A={(1,3), (2,2), (3,1), (2,6), (3,5), (4,4), (5,3), (6,2)} B={(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5), (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6)} Furthermore, A is a subset of B.

  7. Assuming that all outcomes are equally likely, the conditional probability of A given B is:

More Related