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.
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
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
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.
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.
"BBC - Raw - Money - Express Units - Risk." BBC - Homepage . Web. 24 Jan. 2011. < http://www.bbc.co.uk/raw/money/express_unit_risk/ >.
"Earliest Uses of Symbols in Probability and Statistics." Jeff Miller Pages . Web. 24 Jan. 2011. < http://jeff560.tripod.com/stat.html >.
"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 >.
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