How are conditional probability and independent events related? select the correct phrase or notation from each drop-down menu to complete the explanation. the notation __a__ reads the probability of event a given that event b has occurred. if events a and b are independent, then the probability of event b occurring __b__ the probability of event a occurring. events a and b are independent if __c__ a. 1. p(b|a) 2.p(a|b) 3. p(a and b) b. 1. affects 2. does not affect c. 1. p(a|b) = p(a) 2. p(a|b) = p(b) 3. p(a|b) = p(a and b)

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

Use formula for the conditional probability:

Since events A and B are independent, we get

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