1. Probability

2. Today we will look at… 1.Quick Recap from last week 2.Terminology relating to events and outcomes 3.Use of sample spaces when dealing with 2 events 4.Estimating Probabilities from experiments

3. 1.What did we do last week? 1.We discovered that is is equally likely to roll every number on a die 2.We saw that this was only possible when we repeated the experiment several times (350) 3.Relative Frequency = Frequency of the outcome No of Trials

4. 2.Terminology The act of throwing the dice is called the trial The numbers 1,2,3,4,5 and 6 are all the possible outcomes of the trial The required result is called the event

5. Equally Likely Outcomes 2 events are equally likely to occur if they have the same chance of happening

6. Probability In general E represents an event The probability of E occurring is denoted P(E) P(E) = Number of successful outcomes in E Number of Possible outcomes

7. Remember… 1.The probability of an event cannot be less than 0 or more than 1 2.The probability of something that is certain is 1 3.The probability of something impossible is 0

8. 3.Using Sample Spaces When 2 coins are tossed, the set of possible outcomes are (HH,TT,HT,TH) This set of possible outcomes is called the sample space We can use the sample space to calculate probability

9. Using a Table When we have a coin and a dice tossed and thrown at the same time it may be easier to use a table format Dice 123456 CoinHeadH, 1H,2H,3H,4H,5H,6 TailT, 1T,2T,3T,4T,5T,6

10. Try yourself… Make out a sample space for tossing 2 Dice. If the scores are added after the dice are thrown

11. Sample Space for 2 Dice 123456 1234567 2345678 3456789 45678910 56789 11 6789101112

12. 4. Estimating Probabilities from Experiments So far we have calculated probabilities when event are equally likely. However in real life this doesn’t always happen so we need to have another way to estimate probability We may carry out a survey or experiment

14. Expected Frequency To calculate the expected frequency of an event we multiply the probability by the number of trials Eg. A fair coin is tossed 100 times How many heads would you expect to get?

15. Homework Question 6 Page 147 Question 3 and 5 Page 151