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Tutorial 2 - Probability Concepts Original

Tutorial 2 - Probability Concepts Original -...

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CB2201 Sem B in 2012/2013 – TA1, TA3, TA4, TB5, TC4, TF4, TE3, TE4, TE5, TF1, and TF3 CB2201 Topic 2: Probability Concepts 1. Basics of probability theory a. Experiment: An outcome is not known in advance (When an experiment is performed, outcome is known) b. Sample Space (S): The collection of ALL possible outcomes of an experiment c. Event: The collection of SOME possible outcomes of an experiment (An event is said to have occurred when the outcome of the experiment lies in that event) d. Probability: A measure of the possibility that a random phenomenon occurs ۲܍܎ܑܖܑܜܑܗܖ: ܲሺܧݒ݁݊ݐሻ ൌ # ݂ܽݒ݋ݎܾ݈ܽ݁ ݋ݑݐܿ݋݉݁ݏ ݋݂ ݐ݄݁ ݁ݒ݁݊ݐ # ܲ݋ݏݏܾ݈݅݁ ݋ݑݐܿ݋݉݁ݏ ݋݂ ݐ݄݁ ݁ݔ݌݁ݎ݅݉݁݊ݐ , ݓh݁ݎ݁ 0 ൑ ܲݎ݋ܾሺܧݒ݁݊ݐሻ ൑ 1 Example: Toss two coins and we want to know the probability of getting at least one head a. Experiment: Toss two coins b. Sample Space: (4 Possible Outcomes) HH, HT, TH, TT c. Event: Getting at least one head in the experiment (3 Favorable Outcomes) HH, HT, TH d. Probability of getting at least one head ܲሺܩ݁ݐݐ݅݊݃ ܽݐ ݈݁ܽݏݐ ݋݊݁ ݄݁ܽ݀ሻ ൌ # ݂ܽݒ݋ݎܾ݈ܽ݁ ݋ݑݐܿ݋݉݁ݏ ݋݂ ݐ݄݁ ݃݁ݐݐ݅݊݃ ܽݐ ݈݁ܽݏݐ ݋݊݁ ݄݁ܽ݀ # ܲ݋ݏݏܾ݈݅݁ ݋ݑݐܿ݋݉݁ݏ ݋݂ ݐ݋ݏݏ݅݊݃ ݐݓ݋ ܿ݋݅݊ݏ 3 4 2. Mutually Exclusive Events when event A and event B cannot happen together ۲܍܎ܑܖܑܜܑܗܖ: ܲሺܧݒ݁݊ݐ ܣ ܽ݊݀ ܧݒ݁݊ݐ ܤሻ ൌ 0 3. Collectively Exhaustive Events when the list of outcomes in event A and event B is same as Sample Space (S) ۲܍܎ܑܖܑܜܑܗܖ: ܲሺܧݒ݁݊ݐ ܣ ݋ݎ ܧݒ݁݊ݐ ܤሻ ൌ ܲሺܵሻ ൌ 1 4. Complement of the event : the collection of ALL possible outcomes that are not in the event
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