Probability Learning Target: I can find the probability of independent and dependent events. I can find the probability of simple and compound events.

Independent & Dependent Events Events are INDEPENDENT EVENTS if the occurrence of one event does not affect the probability of the other. Events are DEPENDENT EVENTS if the occurrence of one event does affect the probability of the other.

Examples Tell whether each set of events is independent or dependent. Explain your answer. A dime lands heads up and a nickel lands heads up. The result of tossing a dime DOES NOT affect the result of tossing a nickel, so the events are INDEPENDENT. You choose a colored game piece in a board game, and then your sister picks another color. Your sister cannot pick the same color you picked, and there are fewer game pieces for your sister to choose from after you choose, so the events are DEPENDENT.

Your Turn! Tell whether each set of events is independent or dependent. Explain your answer. A number cube lands showing an odd number. It is rolled a second time and lands showing 6. One student in your class is chosen for a project. Then another student in the class is chosen.

Probability of Simple Events Probability- The measure of how likely an event is to occur. It usually is written as a fraction, but can be written as a decimal or percent.

Probability of Simple Events Sample Space – The set of all possible outcomes Favorable – The outcome you’re interested in Ex. The probability of flipping a coin and landing on heads. Sample Space – Heads or Tails Probability=1/2

Probability of Simple Events Rock Paper Scissor Lizard Spock http://www.youtube.com/watch?v=C4PWu5q Z8z8 Sample Space: Rock Paper Scissors Lizard Spock Number of possible outcomes = 5 Prob of Raj throwing paper = Prob of Raj throwing lizard = ⅕ 2. ⅕

Examples Prob of Raj throwing paper or Spock = Prob of Sheldon throwing rock =

Your Turn! Prob of Sheldon throwing paper, scissors, lizard, or Spock= Prob of Sheldon throwing one of the original choices = ⅖ 2. ⅕ 3. ⅘ 4. ⅗

Probability of Simple Events Sample Space for Raj and Sheldon RR RP RS RL RSP PR PP PS PL PSP SR SP SS SL SSP LR LP LS LL LSP SPR SPP SPS SPL SPSP Number of all possible outcomes: 25

Probability of Compound Events Compound Events--An event where there is more than 1 possible outcome. REMEMBER: Independent Events- Events that do not affect each other Independent examples- Rock Paper Scissors Rolling two separate dice Flipping coins Spinning a spinner and rolling a die Compound Independent Probability Method: Compound Independent Probability Probability of (A and B) = (Probability of Event A) x (Probability of Event B)

Sheldon Let’s the Dice Choose Lunch http://www.youtube.com/watch?v=BVIjqd8DBGw Sheldon chooses his entrée by rolling a 20 sided die. There are 5 burgers on this page and 15 other dishes. He then rolls a six sided die to choose his beverage. The beverage choices are lemonade, water, coke, mountain dew, sprite, and sweet tea. Prob of burger=   Prob of lemonade= Prob of both= 5/20=¼ 2. ⅙ 3. ¼*⅙ =1/24 ALSO. DON’T SHOW ENTIRE VIDEO.

Probability of Compound Events Examples- What is the probability of rolling a 6 and a coin landing on heads? Prob of rolling a six = Prob of flipping heads = Prob of both = ⅙ 2. ½ 3. ⅙*½=1/12

Your Turn! Prob of flipping heads = Prob of landing of the 5th step = What is the probability of dropping a coin down 12 stairs and it landing heads up on the 5th stair? Prob of flipping heads = Prob of landing of the 5th step = Prob of both = ½ 2. 1/12 3. ½*1/12=1/24

Probability of Compound Events Dependent Events – Events in which the outcome of one will affect the probability of the other Dependent examples- Picking options out of a hat Picking people out of a crowd Picking cards out of a deck Compound Dependent Probability Method Prob of Events A and B occurring = Prob of Event A*Modified Prob of event B

Probability of Compound Events Examples- There is a bag filled with 10 marbles: 6 red, 1 blue, and 3 green. What is the probability of randomly picking out a red marble then a green marble? Prob of red = Modified prob of green = Prob of both = 6/10=⅗ 2. 3/9=⅓ 3. ⅗*⅓=3/15=⅕

Your Turn! Prob of red = Modified prob of red = There is a bag filled with 10 marbles: 6 red, 1 blue, and 3 green. What is the probability of picking a red then a red then the blue marbles? Prob of red = Modified prob of red = Modified prob of blue = Prob of all = 6/10=⅗ 2. 5/9 3. ⅛ 4. ⅗*5/9*⅛=15/360=1/24

Exit Slip Kahoot--Probability Take this seriously. The top 3 finishers will receive up to 5 bonus points on the test!