Randomness and Probability Section 6 1 1 Starter

Randomness and Probability Section 6. 1. 1

Starter 6. 1. 1 • Let’s play a game with coins! • Toss a coin 4 times and count the number of heads and tails that come up. – For every head, you win $1! – For every tail, you lose $1. • Play the game 10 times at your desk, keeping track of your winnings (or losings!) on each game. • When all are done, you will report your outcomes to me; I will combine so we can see the entire class’ results.

Objectives • Describe what is meant by random outcomes of a trial. • Describe what is meant by the probability of a given outcome.

Randomness • The outcome of some event is considered random if there is no way to tell in advance what the outcome will be for any one trial. • Random does not mean haphazard. – In a large number of trials, there will be some regular distribution of outcomes.

Probability • The probability of an outcome of an event is the proportion of times the particular outcome occurs in many trials of the event. – Note that if the particular outcome always occurs, the proportion would be 1. – Note further that if the outcome never occurs, the proportion would be 0. – In almost all cases, the proportion (and therefore the probability) is between 0 and 1. • So probability is not just a formula: it is an experimentally determined proportion.

Example • What is the probability that a fair coin comes up heads when tossed? • To answer the question, toss a coin many times and find the proportion of heads. • Use the TI Probability Simulator to toss a coin 100 or more times. – Based on the simulation, what is the probability of heads?

Objectives • Describe what is meant by random outcomes of a trial. • Describe what is meant by the probability of a given outcome.

Homework • Read pages 310 – 316 • Do problems 5, 7, 8