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Probability

Probability. PROBABILITY: DEFINITION AND NOTATION. Probability is basically the chance of something happening. It can be calculated from existing statistical data or found by experiment. Sample Space. Sample space.   U   This is the set of all things that can happen. (Outcomes) Examples:

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Probability

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  1. Probability

  2. PROBABILITY: DEFINITION AND NOTATION • Probability is basically the chance of something happening.It can be calculated from existing statistical data or found by experiment.

  3. Sample Space • Sample space.  U   This is the set of all things that can happen. (Outcomes) • Examples: • Rolling a fair dice once.  U = {1,2,3,4,5,6} • Tossing a coin once. U = {Heads, Tails} • Often the sample space may be more complicated than this and we may not always be able to see all the outcomes, hence there are formulas we can use to calculate the probability of something happening. You we see several different ways of calculating probability.

  4. Number of outcomes • Number of outcomes n (U). • Example for rolling a fair dice n (U) = 6 and for tossing a coin n (U) = 2 • The word fair has been used above; it means that there is equal chance for each of the outcomes. • The word biased may be used which means there is not equal chance of each outcome.

  5. Probability Notation • Probability that an event will happen. •  P (A) This represents the probability that event A will happen

  6. PROBABILITY FORMULAE

  7. Probability of events not happening

  8. Probability of events not happening

  9. Probability of A or B happening.

  10. The probability of A and B happening.

  11. Conditional probability • This gives the probability of A happening given B has already happened, this is the condition.

  12. Using Venn Diagrams and Tree diagrams to solve probability questions • There are many probability questions that can be solved using either a table of outcomes, Venn diagrams or Tree diagrams

  13. Examples • The number of students studying Art and Biology was recorded in a Venn diagram as shown below. • (0.20 represents 20% etc. • P = 0.95 • P = 0.25 • P = 0.20 • P = 0.80

  14. Tree Diagrams • Draw a tree diagram that could be used to calculate the probabilities of getting a six when rolling a dice twice (same as rolling two dice once)

  15. Example

  16. Tables of outcomes The table of outcomes is also useful for solving problems like the following: What is the probability of having a score less than five on rolling two dice? See the numbers highlighted in blue

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