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# Sky math challenge 7H

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• 1. Ratios and Probability
• Sky Lee-Math 7H-January 24, 2011
• 2. Why I chose this topic :)
• 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.
• 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.
• I wanted to research and present how Ratios could be used to find the possible outcome of an likely event
• 3. Essential Question : How can Ratios be used to find the probability of a specific outcome of an event?
• 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.
• Ratios help summarize and understand the probable outcome of a likely event in an easy way.
• 4. What is a Ratio?
• A Ratio is a relationship between two amounts showing the number of times one value contains or is contained within the number.
• Ratios can be transformed in to: a fraction and a percentage. -Ratio: 3:5 -Fraction: 3/5 -Percentage: 60%
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?
• Probability is the extent to which something is possible, the possibility of an event occurring against every other outcome.
• Probability is used everyday in our lives, we say we have a lot of luck when the outcome we expected is produced.
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
• 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.
• 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.
• 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.
• 7. Probabilities and Ratios their uses (continued)
• 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.
• Heredity, The child/offspring of the 2 parents will have 1:3 of the mother and the fathers genes and DNA.
• 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.
• 8. Probabilities and Ratios used together
• 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
• 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
• 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
• 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
• I picked a red marble from the cup 7 times out of 15 times
• I picked a yellow marble from the cup 8 times out of 15 times
• So the total ratio is 7:8
• (red marble:yellow marble)
• But the mean Ratio of all the experiments averaged is 2:3
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 :)
• I will pass out dice for each table
• I will pass out a paper for each of you to write on
• Make a table of 7 columns and 2 rows on the sheet of paper
• 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
• Now number your Face of Dice column 1~6
• Roll your dice 36 times and record the outcome of each roll on the number of times rolled column.
• Write the face of dice and next to it the number of times it was rolled.
• Arrange the data for each row and make them into ratios it should be something close to 1:6.
• 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.
• 12. Bibliography
• &quot;Probability.&quot; Wikipedia, the Free Encyclopedia . Web. 24 Jan. 2011. < http://en.wikipedia.org/wiki/Probability >.
•   &quot;BBC - Raw - Money - Express Units - Risk.&quot; BBC - Homepage . Web. 24 Jan. 2011. < http://www.bbc.co.uk/raw/money/express_unit_risk/ >.
• &quot;Earliest Uses of Symbols in Probability and Statistics.&quot; Jeff Miller Pages . Web. 24 Jan. 2011. < http://jeff560.tripod.com/stat.html >.
• &quot;Figures from the History of Probability & Statistics.&quot; Economics :: School of Social Sciences . Web. 24 Jan. 2011. < http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm >.
• &quot;Probability and Statistics EBook - Socr.&quot; Web. 24 Jan. 2011. < http://wiki.stat.ucla.edu/socr/index.php/EBook >.
• 13. Thank you for watching my presentation