Respuesta :
Answer:
If x and y are independent events;
[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]
If x and y are dependent events then;
[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]
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;
[tex]P(x/y)=\frac{P(xny)}{P(y)}=\frac{P(x)*P(y)}{P(y)}=P(x)[/tex]
If x and y are dependent events then;
[tex]P(x/y)=\frac{P(xny)}{P(y)}[/tex]
[tex]P(xny)[/tex] represents the probability of both x and y occurring together;
n denotes intersection
