Question

P(x|y) What is this formula?

Answer 1

Answer:

If x and y are independent events;

$P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)$

If x and y are dependent events then;

$P(x/y)=\frac{P(xny)}{P(y)}$

Step-by-step 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;

$P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)$

If x and y are dependent events then;

$P(x/y)=\frac{P(xny)}{P(y)}$

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

n denotes intersection