Probability What are your Chances?

1. Probability What are your Chances?

2. Overview • Probability is the study of random events. • The probability, or chance, that an event will happen can be described by a number between 0 and 1: • A probability of 0, or 0%, means the event has no chance of happening. • A probability of 1/2 , or 50%, means the event is just as likely to happen as not to happen. • A probability of 1, or 100%, means the event is certain to happen. Can you think of something that has a probability of 0? Can you think of something that has a probability of 1/2? Can you think of something that has a probability of 1?

3. Probability is a number from 0 to 1 that tells you how likely something is to happen. The closer the probability of an event is to 1, the more likely it is that the event will occur. P = 0 0% P = ¼, .25, 25% P = ½, .5 50% P = 1 100% P = ¾, .75 75% Impossible Likely to occur half the time Unlikely Likely Certain

4. Theoretical probability HEADS TAILS P(event) = number of favorable outcomes total number of possible outcomes Tossing a coin and getting a head or a tail is ½ for each since there are only two outcomes. P(head) = ½, 0.5, or 50%. P(tail) = ½, 0.5, or 50%.

5. Sample space: set of all possible outcomes in an experiment.

6. + + + + + = 1 P(4)= {1, 2, 3, 4, 5, 6}

7. 1 6 = = = 1 3 1 6 number of ways to roll the die number of ways to roll the die 6 = = 2 6 number of ways to roll the die You roll a six-sided die whose sides are numbered from 1 through 6. • Find the probability of rolling a 1. • Find the probability of rolling an odd number. Three outcomes correspond to rolling an odd number: rolling a 1, 3, or a 5. number of ways to roll a 1 P (rolling a 1) = • Find the probability of rolling a number less than 7. number of ways to roll an odd number P (rolling odd number) = number of ways to roll less than 7 P (rolling less than 7 ) =

8. Theoretical probability Find the probability of randomly choosing a blue marble from the marbles shown at the right. 3 There are 3 blue marbles. 10 There are 10 marbles in all. ANSWER The probability of choosing a blue marble is , 0.3, or 30%. 3 10 P(blue) =

9. 4 There are 4 green marbles. 10 There are 10 marbles in all. ANSWER 2 The probability of choosing a green marble is ,0.4, or 40%. 5 1. What If you randomly choose a green marble. Find the probability of this event. P(green) =

10. 2 11 1 3 11 11 Daily Homework Quiz Each letter in PROBABILITY is placed in a bag. One letter is randomly chosen from the bag. Find the probability of the event. Write the probability as a fraction. 1. The letter B is chosen. 2. The letter Y is chosen. 3.The letter O or I is chosen.

11. Other examples of theoretical probability are found in determining the probability of drawing a certain card from a standard deck of cards. A standard deck has four suits: spades (), hearts (), diamonds (), and clubs (). It has thirteen cards in each suit: ace, 2, 3, . . ., 10, jack, queen, and king. Each of these cards is equally likely to be drawn.

12. There are 52 cards in a deck. So what are my chances of picking an ace? 4 How many aces are in a deck? 52 How many cards are in a deck? So I have a 4/52 or 1/13 chance of drawing an ace!

13. There are 52 cards in a deck. So what are my chances of picking a face card? 12 How many face cards are in a deck? 52 How many cards are in a deck? So I have a 12/52 or 3/13 chance of drawing a face card!

14. Make a table to organize your outcomes. What is the theoretical probability of rolling a sum of 7 with two die?

15. P(rolling a 7) = 6/36 = 1/6

16. What is the theoretical probability of each outcome below? P(rolling a 2) P(rolling a 3) P(rolling a 4) P(rolling a 5) P(rolling a 6) P(rolling a 7) P(rolling a 8) P(rolling a 9) P(rolling a 10) P(rolling a 11) P(rolling a 12) 1/36 2/36 = 1/18 3/36 = 1/12 4/36 = 1/9 5/36 6/36 = 1/6 5/36 4/36 = 1/9 3/36 = 1/12 2/36 = 1/18 1/36

17. Practice:Measuring Probability Worksheet