2. Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring.  Flip a coin 5 times…  drawing a card, replacing it, drawing again

3. Multiplication Rules for Probability Multiplication Rule 1 When two events are independent, the probability of both occuring is P(A and B) = P(A)P(B)  A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die.  A card is drawn and replaced. Find the probability of drawing a queen and then an ace.  The multiplication rule can be extended to many events…

4. Multiplication Rules for Probability Multiplication Rule 2 when two events are dependent, the probability of both occurring is P(A and B) = P(A)·P(B|A)  P(B|A) is a conditional probability  It means the probability that B occurs given that A has already occurred.

5. Multiplication Rules for Probability examples  A person owns 30 CD’s. 5 of them are jazz. If 2 CD’s are selected at random, what is the probability that both are jazz music? Are the two selections independent?  P(J 1 and J 2 ) =  53% of residents of a city have homeowner’s insurance. Of these 27% also have car insurance. Find P(home ins. and car ins.).

6. Multiplication Rules for Probability  try p 220 # 1 in your notes

7. Multiplication Rules for Probability Conditional Probability The probability that the second event B occurs given that the first event A has occurred is found by: P(B|A) = P(A and B) P(A)

8. Example  P(B and W) is 15/56 and P(B) on the first draw is 3/8. Find the probability of selecting the white chip on the second draw, given that the first chip selected was a black chip.

9.  The probability that Sam parks in a no- parking zone and gets a ticket is 0.06 and the probability that Sam cannot find a parking space and has to park in the no- parking zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no- parking zone. Find the probability that he will get a ticket.

10. “At- least”  A game is played by drawing 4 cards from an ordinary deck and replacing each card after it is drawn. Find the probability that at least 1 ace is drawn. It is easier to find the probability that no aces are drawn and subtract that answer from 1.

11. A coin is tossed 5 times. Find the probability of getting at least 1 tail.

12. Multiplication Rules for Probability turn to page 221  try number 11 in your notes  try number 13

13. Practice  In class p 220 (2-30 even)