Experimental and Theoretical Probability

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Presentation transcript:

Experimental and Theoretical Probability Grade 12 Essential Math

Probability What is probability? Probability is a way to say how likely an event is. Probability is written as a number between 0 and 1 Probability: 0.5 1 Less Likely More Likely Will never happen. Will always happen.

Writing Probability Probability can be written in different ways: As a fraction: 3 5 As words: 3 out of 5 As a decimal: 0.6 As a percent: 60% Easy to convert between these ways! Easy to convert between these ways!

Example There is a 70% chance of rain tomorrow. Write this as: A Decimal A Fraction Words

Probability Probability is how likely an event is. Experimental probability: Probability based on what we have observed in the past Theoretical probability: Probability based on the number of possible events Can be used when we do not have previously observed events Usually, experimental and theoretical probability will be close or the same.

Experimental Probability Experimental Probability is the probability of an event occurring, based on what we have seen happen. To find experimental probability: 𝑃= 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑒𝑣𝑒𝑛𝑡𝑠 𝑡𝑜𝑡𝑎𝑙 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑒𝑣𝑒𝑛𝑡𝑠 Events you want, or are looking for All events you see

Theoretical Probability To find theoretical probability: 𝑃= 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑒𝑣𝑒𝑛𝑡𝑠 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑒𝑣𝑒𝑛𝑡𝑠 Events you want, or are looking for The number of events that can possibly happen

Example In a bowl, there are 4 oranges, 3 apples and 6 bananas. Christina picks a piece of fruit at random. What is the chance that it is an orange? What is the probability of Christina picking a banana? What type of probability is this? (Experimental or theoretical?)

Example Adam and Blake are playing Call of Duty. They record the games and who won: What is the theoretical probability of Adam winning? What is the experimental probability of Adam winning? Game: 1 2 3 4 5 6 7 8 Winner: Adam Blake

Example A die is rolled 542 times and a “6” occurs 151 times. State the theoretical probability of rolling a “6” State the experiment probability. Is it possible that “6” is rolled 12 consecutive times?