Introduction to Probability – Experimental Probability

 What does it mean when you give someone a choice between 2 options and they respond with “flip a coin”?

Investigation: Experimental Probability  How does flipping a coin relate to the gender of a baby?  How likely is it that a family with 3 children has 3 boys?  How could you use coins to simulate this?

Baby Simulation 1.Decide which gender each outcome (heads and tails) will correspond to. 2.Flip 3 coins. Record the results  This represents one family with 3 children 3.Repeat 19 more times. 4.Calculate the experimental probability of 0, 1, 2, 3 heads. 5.Record your results in a table. Number of Heads, XTallyFrequencyP(X) 0II22 / 20 1IIIII II77 / 20 2IIIII III88 / 20 3III33 / 20

Our results: Reflect:  How many different outcomes are there?  Do they have different probabilities? Team1234Total

“Fair game”  A game is fair if…  all players have an equal chance of winning and equal payouts OR  each player can expect to win or lose the same number of times in the long run with equal payouts OR  each player's expected payoff is zero

Are the following games fair? Katie and Jaime:  Roll a die  If a 1, 2 or 3 shows, Katie pays Jaime $1.  If a 4, 5 or 6 shows, Jaime pays Katie $1.  Roll a die  If an odd number shows, Katie pays Jaime $1.  If an even number shows, Jaime pays Katie $2.  Draw cards from a standard card deck  If it’s a red card, Katie pays Jaime $1.  If it’s a spade, Jaime pays Katie $1.  Flip 3 coins  If 3 tails show, Katie pays Jaime $7.5.  Otherwise, Jaime pays Katie $2.5.

Important vocabulary  Trial : one repetition of an experiment  Random variable : a variable whose value corresponds to the outcome of a random event

Important vocabulary  Expected value : the expected outcome of random variable after many repetitions  Event : a set of possible outcomes of an experiment (e.g. drawing a heart)  Simulation : an experiment that models an actual event (e.g. flip a coin to simulate the gender of a baby)

Probability  A measure of the likelihood of an event  based on how often a particular event occurs in comparison with the total number of trials  Probabilities derived from experiments are known as experimental probabilities

Experimental Probability  The observed probability of an event A in an experiment  Written like this: P (A)  Found using this formula: P(A) = number of times A occurs total number of trials *note: probability will always be between 0 and 1 0 = it will never happen 1 = it will happen every time Can be written as a fraction, decimal or percent