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Achint probability powerpoint

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Achint B's probability PowerPoint

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Achint probability powerpoint

  1. 1. Probability By: Achint Bhagat
  2. 2. What Is Probability ? <ul><li>Probability is a numerical measure of the likelihood that an event will occur, or a way of expressing knowledge or belief. For example think about tossing a coin. What are the chances of getting a head and what are the chances of getting a tail? Since tossing a coin has 2 outcomes, either getting a head or a tail and as both are equally likely to occur the probability of getting a head is ½ and the probability of getting a tail is also ½. </li></ul>
  3. 3. History <ul><li>The first scientific treatment was given to the subject by Christian Hyugens in 1657. </li></ul><ul><li>Many mathematician treated the subject as a branch or a follow up of mathematics. </li></ul><ul><li>There have been only two ways to formulize probability, and they are known as the Kolmogorov formulation and the Cox formulation. </li></ul>
  4. 4. What Is Probability? (Part 2) <ul><li>Probability values are always assigned on a scale from 0-1. </li></ul><ul><ul><li>A probability near zero shows an event is unlikely to occur. </li></ul></ul><ul><ul><li>A probability near one indicates an event is almost certain to occur. </li></ul></ul><ul><li>Other probabilities between zero and one show the degree of likelihood that an event will occur. </li></ul>
  5. 5. Experiments and Outcomes <ul><li>What Is an Experiment? </li></ul><ul><li>An experiment is the process by which we generate well defined out comes or i.e. an experiment leads to results called outcomes. </li></ul><ul><li>Outcomes are the results of an experiment and an event is one or more outcomes of an experiment. </li></ul><ul><li>Example: Experiment Outcome </li></ul><ul><li>Toss a coin Head, tail Roll a die 1,2,3,4,5,6 </li></ul><ul><li>Play a football game Win, lose, tie </li></ul><ul><li>Example: The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. If you consider rolling die: The experiment is rolling the die The events are the numbers 1, 2, 3, 4, 5 or 6 and the out come of getting a single number is 1/6 (event/ # is outcomes) </li></ul>
  6. 6. One Very Important Rule <ul><li>One important rule in doing probabilities is, the sum of the probabilities of all elementary events or outcomes is always one. For example consider the experiment of playing a football game which has 3 possible out comes; winning, losing, or a tie. </li></ul><ul><li>The probability of winning is 1/3 </li></ul><ul><li>The probability of losing is 1/3 </li></ul><ul><li>And the probability of a tie is also 1/3 </li></ul><ul><li>If we add all these 3 probabilities we are supposed to get one according to the probability rule Therefore, 1/3+1/3+1/3= 1 </li></ul>
  7. 7. Class Activity <ul><li>The Red Bulls have won 3/5 matches, what is the probability of them wining their next match, (in a percentage)? </li></ul><ul><li>In a black bag there are 2 white marbles, 2 purple marbles, 3 yellow marbles and 1 brown marble. If you pick up a marble without looking at it 8 times what is the probability that a brown marble will appear? </li></ul>
  8. 8. Bibliography <ul><li>http://en.wikipedia.org/wiki/Probability </li></ul><ul><li>http://en.wikipedia.org/wiki/Probability_theory </li></ul><ul><li>http://www.mathgoodies.com/lessons/vol6/intro_probability.html </li></ul><ul><li>http://www.cut-the-knot.org/probability.shtml </li></ul><ul><li>http://mathforum.org/dr.math/faq/faq.prob.intro.html </li></ul>
  9. 9. Thank You For Watching I Hope You Enjoyed and Learned Something New Today!