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# Probability5

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### Probability5

1. 1. WHAT WILL HAPPEN IN 2012?
2. 2. WHICH TEAM WILL WIN WORLD CUP2010?
3. 3. CHAPTER 7 :PROBABILITY
4. 4. Probability IISample space : all the possible outcomes the number of ways achieving success the total number of possible outcomesEvent: the set of outcomes that fulfils a given condition
5. 5. Probability of an event A = the number of ways achieving success the total number of possible outcomes n( A) P ( A) n( S )
6. 6. The Probability of AComplement EventThe complement of an event A- is the set of all outcomes in the sample space that are not included in the outcomes of event A and is written as A’ n( A ) P ( A ) n( S ) P( A ) 1 P( A)
7. 7. The Probability of theCombined EventTwo types of combinationsi. Event A or event B - is the union of set A and set Bi. Event A and event B - the intersection of set A and set B
8. 8. Finding the probability byListing the outcomesA fair coin is tossed and a fair dice is rolled.a. List all the possible outcomes. * You can draw a tree diagram.*b. Find the probability of obtaining a ‘4’ and a ’head’c. Find the probability of obtaining an even number and a tail
9. 9. 1 2 3T 4 5 6 1H 2 3 4 5 6
10. 10.  Sample space S= T ,1 , (T ,2), (T ,3), (T ,4), (T ,5), (T ,6), ( H ,1), ( H ,2), ( H ,3), ( H ,4), ( H ,5), ( H ,6) n(S) = 12 A is an event obtaining a ‘4’ and a ’head’ A = (H,4) n( A) = 1 P(A) = n ( A) = 1 n( S ) 12
11. 11. c. Find the probability of obtaining an even number and a tail. B is an even number and a tail. 3 1 B= (T,2),(T,4),(T,6) 4 12 P(B) = n ( B ) n( S ) = 3 1 12 4
12. 12. Three coins are tossed.a.List all the sample spaceb. Find the probability of getting 2 heads and a tail
13. 13. Tree diagram
14. 14. Finding the probability byListing the outcomes There are 3 balls in a bag: red, yellow and blue. One ball is picked out, and not replaced, and then another ball is picked out.
15. 15. Finding the probability byListing if you throw two dice, what is the probability that you will get the sum of the two numbers is : a) 8, b) 9, c) either 8 or 9?
16. 16. Sample Space of a combinedevent
17. 17. Probability IIIndependent and Dependent EventsSuppose now we consider the probability of 2 events happening. For example, we might throw 2 dice and consider the probability that both are 6s.We call two events independent if the outcome of one of the events doesnt affect the outcome of another. For example, if we throw two dice, the probability of getting a 6 on the second die is the same, no matter what we get with the first one- its still 1/6.
18. 18. Probability II On the other hand, suppose we have a bag containing 2 red and 2 blue balls. If we pick 2 balls out of the bag, the probability that the second is blue depends upon what the colour of the first ball picked was. If the first ball was blue, there will be 1 blue and 2 red balls in the bag when we pick the second ball. So the probability of getting a blue is 1/3. However, if the first ball was red, there will be 1 red and 2 blue balls left so the probability the second ball is blue is 2/3. When the probability of one event depends on another, the events are dependent
19. 19. EXERCISE : SPM QUESTIONS