FOR LEARNING ON JUNE 2nd and 3rd.
Theoretical probability is a method to express the likelihood that something will occur. It is calculated by dividing the number of favourable outcomes by the total possible outcomes.
Step 1) You can view this Khan Academy Video to understand how to calculate the theoretical probability of rolling doubles with 2 six-sided dice.
Looking carefully you can find 6 outcomes that add up to 7: 1&6, 2&5, 3&4, 4&3, 5&2, 6&1
Therefore the Theoretical Probability of rolling a 7 is 6/36 or 1/6.
We write this as P(7) = 1/6 or about 16.7%
Other examples:
P(5) = 4/36 or 1/9 or about 11.1%
P(2) = 1/36 or about 2.3%
Further investigation would confirm that 7 is the most common number when 2 dice are rolled (Lucky Number Seven). This is logical as it is the only outcome that can be made from all possible outcomes of the first die.
ex. If you roll a 1 then a 6 makes seven. If you roll a 3 then 4 can make seven. If you want to roll 6 and you get a 6 on the first die, then you are out of luck. If you want to roll a 9 and you get a 1 or 2 on the first die, again, tough beans.
Experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
Step 3) Roll 2 dice 36 times (each roll is a trial). Keep a tally of how many times you get each value (ex. how many times did you get 5? How many times did you get 7?)
If you don't have dice you can use this dice outcome generator.
Step 4) Calculate the Experimental Probability of rolling a 7. Do this by taking the number of times you rolled a 7 and dividing it by 36. Express as both a fraction in lowest terms and a percent.
ASSESSMENT TASK
In our Google Classroom in Classwork, share and compare your experimental probability of rolling a 7 to the theoretical probability of rolling a 7. Discuss any similarities or differences.
For an extension, do a similar comparison for other values (you will have to accurately figure out those values theoretical probabilities using the above table and the experimental probability from your tallies.
