1. { 11.3 Dependent Events 9.4.3.5 Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems.

2. Guiding Question: How can I know if events are independent or dependent? Lesson Objective: I will be able to determine if events are independent and calculate the probability of the events. Lesson Objective: I will be able to determine if events are independent and calculate the probability of the events. Key Terms Key Terms Independent events Independent events Dependent events Dependent events Conditional probability Conditional probability

3. Guiding Question: How can I know if events are independent or dependent? In blackjack you receive 2 cards and the ideal hand is a sum of 21 (face cards = 10). How could you find this probability? In blackjack you receive 2 cards and the ideal hand is a sum of 21 (face cards = 10). How could you find this probability? Would this be a combination or a permutation? Would this be a combination or a permutation?

4. Guiding Question: How can I know if events are independent or dependent? When 2 or more events happen, you need to determine if they are independent or dependent. When 2 or more events happen, you need to determine if they are independent or dependent. Independent – events have no affect on each other Independent – events have no affect on each other Dependent – one event is conditional on the other. Dependent – one event is conditional on the other. Independent – to find probability you would multiply the probability of each event (with replacement) Independent – to find probability you would multiply the probability of each event (with replacement) P(A and B) = P(A) * P(B) P(A and B) = P(A) * P(B) Ex. Flipping 3 coins, what is the probability of getting 3 heads? Ex. Flipping 3 coins, what is the probability of getting 3 heads? P(heads) * P(heads) * P(heads) = ½ * ½ * ½

5. Guiding Question: How can I know if events are independent or dependent? Dependent – One event can only happen if the first event happens. Dependent – One event can only happen if the first event happens. P(A and B) = P(A) * P(B after A) P(A and B) = P(A) * P(B after A) (without replacement) Ex. If I draw a 2 then I draw a 10? Conditional Probability- P(B|A) = probability of B given that A has occurred. Conditional Probability- P(B|A) = probability of B given that A has occurred. P(B|A) = P(B) * P(A given that B has occurred) P(B|A) = P(B) * P(A given that B has occurred) Ex. P(a king and then a queen) Ex. P(a king and then a queen)

6. Would these events be considered ind. Or dep.? Would these events be considered ind. Or dep.? 1. Tossing 2 dice 2. Drawing an ace, then drawing a king w/out replacement. 3. Flipping a coin and getting heads, rolling a dice and getting a 5. 4. Rolling 2 dice and getting a sum of 7 Guiding Question: How can I know if events are independent or dependent?

7. 2 cards are drawn from a standard deck (52 cards, no jokers). Find the probabilities of the following and classify them as independent or dependent. 2 cards are drawn from a standard deck (52 cards, no jokers). Find the probabilities of the following and classify them as independent or dependent. 1. draw 2 hearts when the 1 st card is replaced 1. draw 2 hearts when the 1 st card is replaced 2. an ace is drawn, not replaced, then a king is drawn. 2. an ace is drawn, not replaced, then a king is drawn.

8. Guiding Question: How can I know if events are independent or dependent? 2 dice are rolled, 1 black and 1 white. Find the probability. 2 dice are rolled, 1 black and 1 white. Find the probability. P(black shows a 4 and the product is less than 20) P(black shows a 4 and the product is less than 20) P(product of 6 & white cube shows 3) P(product of 6 & white cube shows 3) Are these independent or dependent? Why? Are these independent or dependent? Why?

9. Pg. 815-817 10-22 Pg. 815-817 10-22 Day 2 Pg. 815-817 23-30 Day 2 Pg. 815-817 23-30 Assignment