Question

Which of the following are true if events A and B are independent? Select all that apply.
A. P(A | B) = P(A)
B. P(A | B) = P(B)
C. P(A | B) = P(A and B)
D. P(B | A) = P(A and B)
E. P(B | A) = P(A)
F. P(B | A) = P(B)

Answer 1

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,

$P(A\cap B)=P(A)\times P(B)$

The conditional probability of event A given B is computed using the formula:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

And the formula for the conditional probability of event B given A is:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

Consider that events A and B are independent.

Then the conditional probability of event A given B will be:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

             $=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)$

And the conditional probability of event B given A will be:

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

             $=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)$

Thus, the correct statement are (A) and (F).