Question

A random number generator that returns an integer is run twice. Let Event A be an odd number on the first run and Event B be an even number on the second run.

Which statement about the conditional probability is true?




The conditional probability of Event B given Event A is P(B|A)=P(A)P(B) when two events are independent.

The conditional probability of Event B given Event A is P(B|A)=P(B) when two events are not independent.

The conditional probability of Event B given Event A is P(B|A)=P(A and B)P(A) when two events are not independent.

The conditional probability of Event B given Event A is P(B|A)=P(B)P(A) when two events are independent.

Answer 1

Answer: The conditional probability of Event B given Event A is P(B|A)=P(A and B)/P(A) when two events are not independent.

Explanation:

A random number generator that returns an integer is run twice.

Let Event A be an odd number on the first run and Event B be an even number on the second run.

A dependent event is when one event effect the outcome of second event in a context of probability .

Here A is given event which already occurred and probability of getting B after Event A is making events dependent or not independent.

Therefore,the conditional probability of Event B given Event A is P(B|A)=P(A and B)/P(A) =P(A∩B)/P(A).