Applying Ratios to Probability Algebra 4-5

Theoretical Probability Probability P(event) likelihood that an event will occur Outcome result of a single trial (like 1 roll of a die) Event any outcome or group of outcomes Sample Space all of the possible outcomes event sample space favorable outcome rolling an even # 1,2,3,4,5,6 2,4,6

Theoretical Probability P(event) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Can be written as a fraction, decimal, or a percent. Ranges from 0 to 1.  Less likely more likely  |----------------------------|----------------------------| 0 0.5 1 Impossible event Equally likely Certain event and unlikely Rolling 7 (die) flipping a head rolling < 7 (die)

Complement of an Event All outcomes that are not in the event. Sum of Probabilities of event and its complement is 1 P(event) + P(not event) = 1 P(not event) = 1 – P(event)

Experimental Probability P(event) = # 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠 # 𝑡𝑖𝑚𝑒𝑠 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡 𝑖𝑠 𝑑𝑜𝑛𝑒