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- 1. Ratios and Probability <ul><li>Sky Lee-Math 7H-January 24, 2011 </li></ul>
- 2. Why I chose this topic :) <ul><li>I chose Ratios because in our previous unit Comparing and Scaling we used Ratios a lot in our math work and we learned what they were and when they were supposed to be used. </li></ul><ul><li>I chose Probability because this is a subject that was in my math text book (What do you expect?) and I went over the unit and thought it was pretty interesting. </li></ul><ul><li>I wanted to research and present how Ratios could be used to find the possible outcome of an likely event </li></ul>
- 3. Essential Question : How can Ratios be used to find the probability of a specific outcome of an event? <ul><li>I can use Ratios to find the probable outcome of an event, for example rolling a dice there is one event and six outcomes so the ratio of that is 1:6. The probability of me rolling a six in one roll is 1:6. </li></ul><ul><li>Ratios help summarize and understand the probable outcome of a likely event in an easy way. </li></ul>
- 4. What is a Ratio? <ul><li>A Ratio is a relationship between two amounts showing the number of times one value contains or is contained within the number. </li></ul><ul><li>Ratios can be transformed in to: a fraction and a percentage. -Ratio: 3:5 -Fraction: 3/5 -Percentage: 60% </li></ul>Ratios have been around for a long time. Early translators think this word may have been latin, a ratio meaning reason (as in rational). A ratio is a comparison of two numbers using division (part to part or part to whole) A:B Ratios are often expressed in equations and number sentences like this
- 5. What is Probability? <ul><li>Probability is the extent to which something is possible, the possibility of an event occurring against every other outcome. </li></ul><ul><li>Probability is used everyday in our lives, we say we have a lot of luck when the outcome we expected is produced. </li></ul>Probability is a way of expressing knowledge about what will happen or what happened with different variables and various outcomes. Probability is used mainly in these areas of study; Finance, gambling, mathematics, statistics, science and philosophy. But Probability is only a follow up or a branch of mathematics
- 6. Probabilities and Ratios their uses <ul><li>Probability (chance) is very well connected to Gambling games such as poker, slot machines and etc. The idea of probability and chance is used a lot in poker. </li></ul><ul><li>The probability (chance) of Rain falling, and weather forecast is used a lot. When different sets of data is collected and is chosen to the highest Fall of don’t fall ratio. </li></ul><ul><li>Sports, there are probable (estimates) that are taken before a certain match in soccer for example. Experts guess what team might win the world cup, measuring different chances of a goal ratio referring to the past matches and estimating which team will win using probability and ratios. </li></ul>
- 7. Probabilities and Ratios their uses (continued) <ul><li>Soccer, before starting a match the referee decides which team will start by flipping a coin and designating one side of the coin to one team and the other side of the coin to the opposite team so its is fair. </li></ul><ul><li>Heredity, The child/offspring of the 2 parents will have 1:3 of the mother and the fathers genes and DNA. </li></ul><ul><li>Voting, for example when there is an election going on in a certain country, there will be one person who is leading the other person running by at least a little bit. Like there would be a ratio of votes counted. The ratio of democratic seats in the Parliament to the republican house is 6:4. </li></ul>
- 8. Probabilities and Ratios used together <ul><li>The Probability of flipping a coin and getting heads is 1 out of 2 times. Because there is 1 coin and 2 outcomes so the Ratio of getting a heads to a tails from flipping a coin is 1:2 </li></ul><ul><li>The Probability in rolling a dice and getting 6 is 1 out of 6 times. Because there is 1 die and 6 outcomes. The Ratio of getting a 6 from rolling a dice once is 1:6 </li></ul><ul><li>The Probability in getting in picking a Ace of Hearts in a deck of cards is 1 of 54 times because you have one chance to pick a card but 54 different out comes. The Ratio of picking a Ace of Hearts in a deck of cards is 1:54 </li></ul>
- 9. Experiments Conducted Number of One’s rolled)xxxxxxx:7 Number of Two’s rolled)xxxxxx:6 Number of Three’s rolled)xxxxx:5 Number of Four’s rolled)xxxxxx:6 Number of Five’s rolled)xxxxxxx:7 Number of Six’s rolled)xxxxx:5 Ratio of Outcomes: 7:6:5:6:7:5 rolled 36 times The Ratio of Rolling a 1 is 1:6 The Ratio of Rolling a 2 is 1:6 The Ratio of Rolling a 3 is 1:6 The Ratio of Rolling a 4 is 1:6 The Ratio of Rolling a 5 is 1:6 The Ratio of Rolling a 6 is 1:6 For Example there is 1 die and 6 sides: There are 6 possible outcomes Face of Dice Number of times rolled 1 7 2 6 3 5 4 7 5 6 6 5
- 10. Experiments Conducted For example there are 10 fur balls in a cup Red and Yellow there are 2 different colors of marbles. Average Ratio: 2:3 Red 2:3 Yellow The estimated amount of yellow fur balls in the cup is 6 The estimated amount of red fur balls in the cup is 4 The probability of picking a Yellow fur ball is 6 out of 10 times The probability of picking a Red fur ball is 4 out of 10 times <ul><li>I picked a red marble from the cup 7 times out of 15 times </li></ul><ul><li>I picked a yellow marble from the cup 8 times out of 15 times </li></ul><ul><li>So the total ratio is 7:8 </li></ul><ul><li>(red marble:yellow marble) </li></ul><ul><li>But the mean Ratio of all the experiments averaged is 2:3 </li></ul>Red Yellow Ratio Trial 1 3 2 3:2 Trial 2 2 3 2:3 Trial 3 2 3 2:3
- 11. Classroom activity Now we will conduct an experiment/roll a dice :) <ul><li>I will pass out dice for each table </li></ul><ul><li>I will pass out a paper for each of you to write on </li></ul><ul><li>Make a table of 7 columns and 2 rows on the sheet of paper </li></ul><ul><li>Write Face of Dice on the first row on the left side and Number of times rolled on the right side of the first row </li></ul><ul><li>Now number your Face of Dice column 1~6 </li></ul><ul><li>Roll your dice 36 times and record the outcome of each roll on the number of times rolled column. </li></ul><ul><li>Write the face of dice and next to it the number of times it was rolled. </li></ul><ul><li>Arrange the data for each row and make them into ratios it should be something close to 1:6. </li></ul><ul><li>The basic lesson of this activity was to teach that Ratios can be used to help understand the possible outcomes of an event to occur. </li></ul>
- 12. Bibliography <ul><li>"Probability." Wikipedia, the Free Encyclopedia . Web. 24 Jan. 2011. < http://en.wikipedia.org/wiki/Probability >. </li></ul><ul><li> "BBC - Raw - Money - Express Units - Risk." BBC - Homepage . Web. 24 Jan. 2011. < http://www.bbc.co.uk/raw/money/express_unit_risk/ >. </li></ul><ul><li>"Earliest Uses of Symbols in Probability and Statistics." Jeff Miller Pages . Web. 24 Jan. 2011. < http://jeff560.tripod.com/stat.html >. </li></ul><ul><li>"Figures from the History of Probability & Statistics." Economics :: School of Social Sciences . Web. 24 Jan. 2011. < http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm >. </li></ul><ul><li>"Probability and Statistics EBook - Socr." Web. 24 Jan. 2011. < http://wiki.stat.ucla.edu/socr/index.php/EBook >. </li></ul>
- 13. Thank you for watching my presentation

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