Aim: How do we find the probability of compound events? 1) How many pounds is 24 ounces? 1 pound = 16 ounces 2) Evaluate 3y – 7, when y = 5. 3) Solve and graph 2c – 7 ≥ 9. Do Now

Aim: How do we find the probability of compound events? Independent Events- when the outcome of one event does not affect the likelihood of the other event Compound Events- the outcome of two events Dependent Events- when the outcome of one event does affect the likelihood of the other event Vocabulary

Aim: How do we find the probability of compound events? The probability of choosing two red gumballs with replacement is different than the probability without replacement. You randomly choose two gumballs one at a time from the jar below.

Aim: How do we find the probability of compound events? Independent Events P (red) = 2 5 first event second event P (red) = 2 5 You replace the gumball, so the probability of choosing a red is the same each time. Dependent Events P (red) = 2 5 first event second event P (red) = 1 4 You do not replace the gumball, so the probability of choosing a red changes.

Aim: How do we find the probability of compound events? Practice: Tell whether the events are independent or dependent. a) You roll a number cube. Then you roll the number cube again. b) You randomly draw a number from a bag. Then you randomly draw a second number without putting the first number back. Independent Event- The results of the first roll does note effect the results of the second time the number cube is rolled. Dependent Event- The results of the first draw effects the results of the second time a number is drawn because the number is not being replaced.

Aim: How do we find the probability of compound events? Example : Find the probability of choosing two red gumballs with replacement.. Probability of Independent Events (with replacement) If events A and B are independent, then P(A and B) = P(A) P(B). P (red and red, with replacement) = 2 5 = 4 25 ∙ 2 5

Aim: How do we find the probability of compound events?. Probability of Dependent Events (without replacement) If events A and B are dependent, then P(A and B) = P(A) P(B given A) Example : Find the probability of choosing two red gumballs without replacement... P (red and red, without replacement) = 2 5 = 2 20 ∙ 1 4

Aim: How do we find the probability of compound events? Practice - Find the probability of the following events.... 1) P (blue and blue, with replacement) = 3 5 = 9 25 ∙ ) P (blue and blue, without replacement) = 3 5 = 6 20 ∙ ) P (red and blue, without replacement) = 2 5 = 6 20 ∙ 3 4

Aim: How do we find the probability of compound events? 1) A box contains 3 pens, 2 markers, and 1 highlighter. Tara selects one item at random and does not return it to the box. She then selects a second item at random. What is the probability that Tara selects a pen and then a marker? (2008) P (pen and marker, without replacement) = 3 6 = 6 30 ∙ 2 5 = 1 5

Aim: How do we find the probability of compound events? 2) Keisha has one penny, two nickels, and one dime in her pocket. She randomly takes one coin out of her pocket. She puts it back and randomly takes out another coin. What is the probability that Keisha selects a nickel and a dime. P (nickel and dime with replacement) = 2 4 = 2 16 ∙ 1 4 = 1 8

Aim: How do we find the probability of compound events? 3) Eric's mother wants to help him with his math homework. She puts 24 cookies in a cookie jar. Twelve of the cookies are chocolate chip, 8 are oatmeal, and 4 are peanut butter. She then has Eric select two cookies from the jar without looking. If Eric does not replace his first selection: What is the probability Eric will pick: a) an oatmeal cookie first and a chocolate chip cookie second? b) an oatmeal cookie first and an a oatmeal cookie second? b) an oatmeal cookie first and an a peanut butter cookie second? If Eric does replace his first selection: What is the probability Eric will pick: a) an oatmeal cookie first and a chocolate chip cookie second? b) an oatmeal cookie first and an a oatmeal cookie second? b) an oatmeal cookie first and an a peanut butter cookie second?

Aim: How do we find the probability of compound events? 4) You roll a number cube twice. What is the probability of rolling a '5' the first time and then a '5' the second time. 5) You have a penny and a nickel. What is the probability of rolling a '5' the first time and then a '5' the second time.