Experimental and Theoretical Probability

Definitions Probability – the likelihood of an event occurring. Notation – P(event) Equation – P(event)=

Types of Probability Experimental Probability – the probability of a future event predicted by a number of observations of past events. Theoretical Probability – the probability of a future event based upon controlled or ideal conditions. If an infinite number of observations could be made, then Experimental and Theoretical Probabilities will be equal.

Fractions, Decimals, and Percents The probability equation gives the answer as a fraction, but the answer to a probability question can take the form of a fraction, decimal, or percent. To convert to a decimal, simply divide the top number (numerator) by the bottom number (denominator). To convert to a percentage, first convert to a decimal, then multiply by 100%. Ex. 3/8 = 0.375 = 37.5%

Example: Experimental Probability The following table shows the results from the roll of a die. The total number of rolls is 12+11+14+12+11+13=73. What is: P(3)? 14/73 P(1,2,3)? (12+11+14)/73=37/73 P(even)? (11+12+13)/73=36/73 Die Roll Outcome Frequency 1 12 2 11 3 14 4 5 6 13

Example: Theoretical Probability Suppose you have a die with six sides. (Six possible outcomes). What is: P(3)? 1/6 P(1,2,3)? 3/6 = 1/2 P(1 or 2)? 2/6=1/3

Using Probability to Make Predictions If you know the probability of a event, multiply its decimal equivalent by the number in another sample size. For Example: If, on average, 45 out of 100 (or 45%) people pay for their lunch with exact change, how many people out of the 120 who eat at the Harvest Café this week will pay with exact change? Decimal Equivalent = 45/100 = .45 x New Group Number = .45 x 120 = 54 people

Assignment Worksheets on Theoretical and Experimental Probability Note: Prime numbers are; 2, 3, 5, 7, 11, 13. Note: Perfect Squares are 1, 4, 9, 16