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# Probability Powerpoint

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• Best one to Basic Probability Theory

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### Probability Powerpoint

1. 1. PROBABILITY! Notes Examples Sample Problems
2. 2. Definition <ul><li>Probability is the measure of how likely something will occur. </li></ul><ul><li>It is the ratio of desired outcomes to total outcomes. </li></ul><ul><ul><li>(# desired) / (# total) </li></ul></ul><ul><li>Probabilities of all outcomes sums to 1. </li></ul>
3. 3. Example <ul><li>If I roll a number cube, there are six total possibilities. (1,2,3,4,5,6) </li></ul><ul><li>Each possibility only has one outcome, so each has a PROBABILITY of 1/6. </li></ul><ul><li>For instance, the probability I roll a 2 is 1/6, since there is only a single 2 on the number cube. </li></ul>
4. 4. Practice <ul><li>If I flip a coin, what is the probability I get heads? </li></ul><ul><li>What is the probability I get tails? </li></ul><ul><li>Remember, to think of how many possibilities there are. </li></ul>
5. 5. Answer <ul><li>P(heads) = 1/2 </li></ul><ul><li>P(tails) = 1/2 </li></ul><ul><li>If you add these two up, you will get 1, which means the answers are probably right. </li></ul>
6. 6. Two or more events <ul><li>If there are two or more events, you need to consider if it is happening at the same time or one after the other. </li></ul>
7. 7. “And” <ul><li>If the two events are happening at the same time, you need to multiply the two probabilities together. </li></ul><ul><li>Usually, the questions use the word “and” when describing the outcomes. </li></ul>
8. 8. “Or” <ul><li>If the two events are happening one after the other, you need to add the two probabilities. </li></ul><ul><li>Usually, the questions use the word “or” when describing the outcomes. </li></ul>
9. 9. Practice <ul><li>If I roll a number cube and flip a coin: </li></ul><ul><li>What is the probability I will get a heads and a 6? </li></ul><ul><li>What is the probability I will get a tails or a 3? </li></ul>
10. 10. Answers <ul><li>P(heads and 6) = 1/2 x 1/6 =1/12 </li></ul><ul><li>P(tails or a 5) = 1/2 + 1/6 = 8/12 = 2/3 </li></ul>
11. 11. Experimental Probability <ul><li>An experimental probability is one that happens as the result of an experiment. </li></ul><ul><ul><li>(# of outcomes) / (# of trials) </li></ul></ul><ul><li>The probabilities we have done so far are “theoretical probabilities”, because there was no experiment. </li></ul>
12. 12. Experiment <ul><li>Flip a coin 50 times, and write down what happens for each flip. </li></ul><ul><li>In the end, find the experimental probabilities by writing the how many times heads and tails occurred over the total number of trials (flips) </li></ul>