Question

P(x|y)
What is this formula?

Answer 1

If x and y are independent events;

`P(x/y)=(P(xny))/(P(y))=(P(x)*P(y))/(P(y))=P(x)`

If x and y are dependent events then;

`P(x/y)=(P(xny))/(P(y))`

Explanation:

The expression;

P(x|y) in probability represents the conditional probability of an event x occurring given that an event y has already occurred. An example of such would be; the probability that a student passes the examination given that he attempted all the assignments.

If x and y are independent events, that is the occurrence of y does not in any way influence the occurrence of x, then;

`P(x/y)=(P(xny))/(P(y))=(P(x)*P(y))/(P(y))=P(x)`

If x and y are dependent events then;

`P(x/y)=(P(xny))/(P(y))`

`P(xny)` represents the probability of both x and y occurring together;

n denotes intersection