Lesson 71- The event a and b

When do you multiply probabilities?
Situation 1: Drawing two balls from the pot, without replacement.
A: the first ball is white                                Find: P(a) = 2/3      P(B given that the first ball drawn is white)
B: the second ball is black                                                         = P( b | a) = 1/2

* note: using a tree diagram for this question will be useful!

Multiplication Law:
General Case: P( a and b) = P(a) x P(B|A)

Equivalently:  p(b | a) = P (A and B)
                                       P(A)
Special Sub-case:  Events A and B are independent if p(B | A) = P(b)
                            For independent events: P(a and b) = p(a) x p(b)
Two events that are not independent are called dependent

Example:
Three cards are drawn with replacement from a shuffled deck of 52 cards
What is the probability that all three are spades?
P (S and S and S) = 13/52 x 12/51 x 11/50 = 11/850