Conditional Probability A conditional probability is the probability of an event occurring, given that another event has already occurred. The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B/A) and is read as “probability of B, given A.”

Conditional Probability Make up some card problems. Explain how a card deck is put together P(K given a Q was selected and not returned) P(K given a K was selected and not returned) P(K given hearts) P(red face card given 3 black face cards are gone) Assume we have buckets of marbles of different colors and make up some examples Use table on page 115

Independent and Dependent Events Two events are independent if the occurrence of one of he events does not affect the probability of the occurrence of the other event. Two events A and B are independent if P(B/A) = P(B) or if P(A/B) = P(A) Events that are not independent are dependent.

Are the following Independent and Dependent Events? Selecting cards with replacement Selecting cards w/o replacement Rolling a die and picking a card Graduating HS and going to college Making a pie and eating it Learning to ride a horse and playing golf Making parts and then assembling them Learning to drive a car and getting a good grade on you math test. Practice piano and being a concert pianist

Multiplication Rule for the Probability of A and B The probability that two events A and B will occur in sequence is P(A and B) = P(A)  P(B/A) If events A and B are independent, then the rule can be simplified to P(A and B) = P(A)  P(B) This simplification rule can be extended for any number of events.

Determine if the following dependent or not, then find the probability Drawing a king then a queen Drawing a face card and rolling more than 6 on a pair of die Drawing 3 hearts in sequence Drawing 3 deuces in sequence