Answer:
The correct statement are (A) and (F).
Step-by-step explanation:
Events A and B are independent or mutually independent events if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.
That is,
[tex]P(A\cap B)=P(A)\times P(B)[/tex]
The conditional probability of event A given B is computed using the formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
And the formula for the conditional probability of event B given A is:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
Consider that events A and B are independent.
Then the conditional probability of event A given B will be:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)[/tex]
And the conditional probability of event B given A will be:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)[/tex]
Thus, the correct statement are (A) and (F).
