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- 1. STF 1093 Statistics for Biology<br />LU2: Basic Probability<br />
- 2. Learning Objectives<br />At the end of this learning unit, the students must be able to:<br />Define experiment, outcome, event, probability and equally likely.<br />Restate the formula for finding the probability of an event.<br />Determine the outcomes and probabilities for experiments.<br />Recognize the difference between outcomes that are equally likely and not equally likely to occur.<br />Apply probability concepts to complete exercises.<br />
- 3. 5.1 The Meaning of Probability<br />3<br />Probability is used to describe RANDOMor CHANCESof events to occur. <br /> <br />Every day we are faced with probability statements involving the words:<br />1. What is the likelihood that X will occur?<br />2. What is the chance that Brazil will win the 2010 World Cup?<br />3. The upgrading of KuchingAirport will likely be completed on time.<br />4. There is a 50-50 possibilitythat an electricity trip will occur.<br />
- 4. Let’s Recall…<br />http://www.youtube.com/watch?v=GH0BWluXxtM&feature=related<br />
- 5. 5<br /><ul><li>An event is some specified result that may or may not occur when an experiment is performed.
- 6. For example, in an experiment of tossing a coin once, the coin landing with heads facing up is an event, since it may or may not occur.
- 7. The probability of an event is a measure of the likelihood of its occurrence. Probability is always expressed as a decimal and it will always fall between 0 and 1.</li></ul>Probability near 0 indicates that the event is very unlikely to occur. Zero (0) probability (p = 0) indicates that the event is certain not to occur. <br /> <br />Probability near 1 suggests that the events is quite likely to occur. A probability of one (p = 1) indicates that the event is certain to occur.<br />
- 8. 5.2 The Equal-Likelihood Model<br />6<br /><ul><li>This model applies when the possible outcomes of an experiment are equally likely to occur.
- 9. Suppose there are N equally likely possible outcomes from an experiment.
- 10. Then the probability that a specified events equals the number of ways, f, that the event can occur, divided by the total number, N, of possible outcomes. </li></li></ul><li>7<br />The probability is<br />f = No. of ways event can occur<br />N = Total number of possible outcomes.<br />In other words, in a situation where several different outcomes are possible, we define the probability for any particular outcome as a fraction of the proportion.<br />Example 1<br />http://www.youtube.com/watch?v=wuyBEhMo5ZA&feature=related<br />
- 11. 8<br />Example 2. A jar contains 1000 marbles, 800 are black and 200 are red. What is the probability of drawing a black marble out of the jar.<br />Solution: <br />Here 800 is the number of possible outcomes, f<br />The total number of possible outcomes is 1000, N<br />Thus the probability is<br /> and<br />The probability of drawing a black marble is much higher than the probability of you picking a red marble because there are more black marbles in the jar.<br />
- 12. Let’s Play!Probability Game<br />http://www.youtube.com/watch?v=V6Ih87xLQfo<br />
- 13. 10<br /> 5.3 Basic Probability Theorems<br />Addition Theorems<br />If event A and event B are mutually exclusive, then<br />P(A or B) = P(A) + P(B) <br />A<br />B<br />Because event A and event B are<br />mutually exclusive, the total coloured<br />region equal to the sum of the two <br />coloured disks.<br />For mutually exclusive events<br /> Illustrated by Venn diagram<br />More generally if events A, B,C…..are mutually exclusive, then<br /> <br />P(A or B or C ….) = P(A) + P(B) + P(C) + ……..<br />
- 14. 11<br />For non-mutually exclusive events, then<br />(A and B) – joint occurrence<br />(A or B)<br />The general addition rule,<br /> If A and B are two events then<br /> P(A or B) = P(A) + P(B) – P(A and B)<br />The general notation is<br />Probability of A B events to occur<br /> P(A B) = P(A) + P(B) – P(A B)<br />
- 15. Exercises for this week<br />Check for weekly task in STF1093 Group in Facebook<br />http://www.facebook.com/groups/140090106073688<br />
- 16.
- 17. Thank You!Any suggestions or comments??<br />

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