Probability5
Download as PPTX, PDF1 like881 views
This document discusses probability and related concepts like sample space, events, and dependent and independent events. It provides examples of calculating probabilities by listing outcomes and constructing tree diagrams for combined events. It also discusses the probability of complementary events and the probability of unions and intersections of events. Examples include calculating the probability of obtaining certain numbers when rolling dice or outcomes when drawing balls from bags. The document emphasizes that two events are independent if the outcome of one does not affect the other, while dependent events influence each other's probabilities.
Probability5
- 1. WHAT WILL HAPPEN IN 2012?
- 2. WHICH TEAM WILL WIN WORLD CUP 2010?
- 4. Probability II Sample space : all the possible outcomes the number of ways achieving success the total number of possible outcomes Event: the set of outcomes that fulfils a given condition
- 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. The Probability of A Complement Event The 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. The Probability of the Combined Event Two types of combinations i. Event A or event B - is the union of set A and set B i. Event A and event B - the intersection of set A and set B
- 8. Finding the probability by Listing the outcomes A 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. 1 2 3 T 4 5 6 1 H 2 3 4 5 6
- 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. 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. Three coins are tossed. a.List all the sample space b. Find the probability of getting 2 heads and a tail
- 13. Tree diagram
- 14. Finding the probability by Listing 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.
- 16. Finding the probability by Listing 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?
- 17. Sample Space of a combined event
- 18. Probability II Independent and Dependent Events Suppose now we consider the probability of 2 events happening. For example, we might throw 2 dice and consider the probability that both are 6's. We call two events independent if the outcome of one of the events doesn't 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- it's still 1/6.
- 19. 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
- 21. EXERCISE : SPM QUESTIONS