1. Probability Learning Outcomes  I can find the probability of simple events, combined events and use expectation  I can use the addition rule for Mutually exclusive events  I can understand Independent events and determine the probability of 2 independent events occurring  I can use a probability tree to illustrate events  I can understand Dependent events

2. Probability Probability is how likely an event is to happen P(event) = No. of desired outcomes total No. of outcomes Example: A dice is thrown. The probability of getting a 3: P(3) = The probability of an even number P(even) =

3. 123456 1 2 3 4 5 6 Probability Combined Events Sample space ( A probability space diagram) Example Two dice are rolled and the numbers on each dice are added i)Complete the probability space diagram below ii)Find a) P(total = 6) b) P(total is even) c) P(total ≥ 8) First die Second die

4. Probability Mutually Exclusive Events Head and Tail are mutually exclusive events when a coin is tossed Mutually exclusive – one or other of the events happen, not both. Keyword is ‘OR’ Example Rolling a die - 6 OR not 6: not getting = 1 Getting a red card - red OR not red: = 1 Being sunny today - sun OR no sun: = 1 P(event) = 1 – P( )

5. Probability Mutually Exclusive Events Example 1) Rolling a die P(5 or 6) = 2) Probability of not raining in June given P(rain) = 0.3 P( ) =

6. Probability Independent Events Events are unrelated Keyword is ‘AND’ P(A and B) = P(A) x P(B) P(Rain on a given day) = 0.3P(Tuesday) = 1 / 7 P(Rain and Tuesday) = A coin is tossed and a die is rolled. Find: P(Head and 6) =

7. Probability Tree Diagrams 1.A bag has 5 green balls and 4 red balls. Two balls are selected at random with replacement. i.List the 4 possible outcomes ii.Find P(2 red) iii.P(1 of each colour) iv.P(2 green) G R G R G R P(G) = 5 / 9 P(R) = 4 / 9 P(2 Red) = P(1 of each colour) = P(2 green) =

8. Probability Tree Diagrams 1.A bag has 5 green balls and 4 red balls. Two balls are selected at random without replacement. i.List the 4 possible outcomes ii.Find P(2 red) iii.P(1 of each colour) iv.P(2 green) G R G R G R

9. Probability Tree Diagrams that lead to quadratic equations When a piece of toast is dropped it is more likely to land buttered side down. When it is dropped twice the probability that it will only land once buttered side down is 0.48. What is the probability that it will land buttered side down after it is dropped only once? P(B) Buttered side down P(B) Buttered side up B B B B B B

10. Probability Additional Notes

11. Probability  I can find the probability of simple events, combined events and use expectation  I can use the addition rule for Mutually exclusive events  I can understand Independent events and determine the probability of 2 independent events occurring  I can use a probability tree to illustrate events  I can understand Dependent events Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further         