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# Probability

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Everything Maths, Grade 10. Chapter 10: Probability.

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### Probability

1. 1. 1 Everything Maths www.everythingmaths.co.za 14. Probability Grade 10
2. 2. 2 Everything Maths www.everythingmaths.co.za Terminology ● An experiment refers to an uncertain process. ● An outcome of an experiment is a single result of that experiment. ● The sample space of an experiment is the set of all possible outcomes of that experiment. The sample space is denoted with the symbol S and the size of the sample space (the total number of possible outcomes) is denoted with n(S) ● An event is a specific set of outcomes of an experiment that you are interested in. An event is denoted with the letter E and the number of outcomes in the event with n(E).
3. 3. 3 Everything Maths www.everythingmaths.co.za Theoretical probability ● A probability is a real number between 0 and 1 that describes how likely it is that an event will occur. A probability can also be written as a percentage or as a fraction. ● A probability of 0 means that an event will never occur and a probability of 1 means that an event will always occur. A probability of 0,5 means that an event will occur half the time. ● The probability of an event is the ratio between the number of outcomes in the event set and the number of possible outcomes in the sample space: Relative frequency ● The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted.
4. 4. 4 Everything Maths www.everythingmaths.co.za Venn diagrams A Venn diagram is a graphical way of representing the relationship between sets.In each Venn diagram a set is represented by a closed curve. The region inside the curve represents the elements that belong to the set, while the region outside the curve represents the elements that are excluded from the set.
5. 5. 5 Everything Maths www.everythingmaths.co.za Union and intersection ● The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A B.∪ ● The intersection of two sets is a new set that contains all of the elements that are in both sets. The intersection is written as A ∩ B. ● Union and intersection: P (A B) = P (A) + P (B) − P (A ∩ B).∪
6. 6. 6 Everything Maths www.everythingmaths.co.za
7. 7. 7 Everything Maths www.everythingmaths.co.za Probability identities ● The probability of sample space: P(S) = 1. ● P (A B) = P (A) + P (B) − P (A ∩ B).∪
8. 8. 8 Everything Maths www.everythingmaths.co.za Mutually exclusive events Mutually exclusive events are two events that cannot occur at the same time. Whenever an outcome of an experiment is in the first event, it can not also be in the second event.
9. 9. 9 Everything Maths www.everythingmaths.co.za Complementary events ● The complement of a set, A, is a different set that contains all of the elements that are not in A. We write the complement of A as A', or sometimes as “not (A)”. ● Complementary events are mutually exclusive: A ∩ A' = ∅ ● Complementary events cover the sample space: A A' = S∪ ● Probabilities of complementary events sum to 1: P (A) + P (A' ) = P (A A' ) = P (S) = 1∪
10. 10. 10 Everything Maths www.everythingmaths.co.za For more practice see: www.everythingmaths.co.za