Conditional Probability

1. 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.”

2. 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

3. 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.

4. 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

5. 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.

6. 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