BellWork

1. What is the probability of the following: Rolling a 4 on a die Rolling an even number on a die Rolling a number greater than 2 on a die Answer the following: BellWork

2. How to Hit it Bigin the Lottery! Probability of Compound Events

3. Students play in pairs and take turns. • After rolling the number cubes, Player 1 records the sum of the numbers. • Player 1 can continue as long as desired or until the sum of the number cubes is eight. If the sum is eight, the player loses all points for that round. If the player stops before getting a sum of eight, the players record the total of all points for the round. • Player 2 does the same. • Both players use the chart to keep a running total of points. • The player with the most points at the end wins! Directions

4. Review: ASimple Eventhas only one outcome. • New Info: A Compound Eventis a combination of at least two simple events. • There are two kinds of compound events: • Independent Events - When the outcome of the first event has no influence on the likelihood of a future event occurring. • Dependent Events - When the outcome of the first event reduces the amount of possible outcomes (and as a result, the likelihood) of future event(s). Probability of Compound Events

5. Review of a Simple Event What is the probability of rolling less than a 5?

6. To determine the probability of a compound event, multiply the probabilities of the individual events. Example: What is the probability of drawing a Queen and then a King? There are 52 cards in a deck and in it are 4 Queens as well as 4 Kings. So the odds are 4/52 (simplified to 1/13) Compound Events

7. Probability of a single event Probability of the compound event 1/169 = 0.0059 (about six thousandths) This one is less than 1/10… • 1/13 = 0.063 • (about six hundredths) of this one! Key Difference!

8. To win, you must first spin a number higher than 7, and then then spin an even number. • Your probability … • A fair spinner is one on which all the sections are the same size. • A fair competition is one in which everyone has the same probability of winning. Spinner Probability

9. Abbreviations are used to illustrate what happens when we solve probabilities. • P: Means total probability • A: Refers to the first event • B: Refers to the second event • Probability that 2 independent events will take place: • P(A&B) = P(A)P(B) • The probability of A and B both happening equals the probability of A times the probability of B. • Probability that 2 dependent events will take place: • P(A&B) + P(A)P (B following A) • The probability of A & B happening equals the probability of A times the probability of B after A has happened. Dependent Events

10. “Example: You share your last jelly beans with a friend. • There are 12 jelly beans left over. • Both of you like the red beans most. There are only 2. • Your friend is next get to take two beans. • What is the probability that she can get both red beans? Dependent Events Note the pattern: P(A&B) = P(A)P(B following A)

11. There are 12 marbles in the bag: • 2 Blue • 3 Yellow • 3 Green • 4 Red • Your friend is to reach in and try to take out a yellow marble. He will keep it out. You will try to the same with a red marble. What is the probability of success? Practice

12. You will pick out three numbers between 1 and 30. • You may only use a number once. • If you pick the three winning numbers I have pre-selected, you will win the Grand Prize. • But, in order to submit your numbers and compete, you must also determine in writing the probability of winning. • You have 3 minutes to choose your numbers and figure out the probability. Lucky Lottery Do Not Click Again until ready to reveal probability

13. Assignment