Question

7. What is the difference between P(A) and P(A|B)? Give an example to illustrate your point. thank you

Answer 1

P(A) is the probability that event A occurs

P(A given B) is the probability that A occurs if B also occurs (conditional probability).

Example:

70% of people like Chocolate, and 35% like Chocolate AND like Strawberry.

Let A be the event that people like chocolate.

P(A) = 0.70

and B be the event that people like strawberry.

P(A and B) = 0.35

Probability that a friend like strawberry given that he a friend also like chocolate, P(A | B) is

P(A | B) = P(A and B) / P(A)

             = 0.35 / 0.7

             = 0.50

Probability that a friend like strawberry given that he a friend also like chocolate is 0.50

P(A | B) may or may not be equal to P(A) (the unconditional probability of A).

If P(A | B) = P(A), then events A and B are said to be "independent"