Question

How are conditional probability and independent events related?

Answer 1

Answer:

1. P(A|B) - option 2

2. does not affect - option 2

3. P(A) - option 1

Step-by-step explanation:

By the definition, the notation P(A|B) reads the probability of event A given that event B has occured. So, for the first gap correct choice is 2 - P(A|B).

If events A and B are independent, then the probability of event B occuring does not affect the probability of event A occuring. So, for the second gap correct choice is 2 - does not affect.

Events A and B are independent, then

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

Use formula for the conditional probability:

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

Since events A and B are independent, we get

$P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)$

So, for the third gap correct answer is 1 - P(A)