Transcript Probability
Probability What’s the probability? • What are the chances that a person will experience death and taxes? • How likely is it that the President will talk to Congress tomorrow? • Is it probably going to rain over the weekend? • What is the likelihood that the Red Wings will win the Stanley Cup? How probable is it…? • • • • • • … the sun rising tomorrow? … capturing the Loch Ness Monster? … taxes going up? … taxes going down? … a sixth grader to run a 3-minute mile? … throwing “snake eyes” in one roll of two dice? Probability Words No Chance Low Probability Even Chance High Probability Certainty Never Not Likely Toss-Up Likely Always Impossible Improbable Maybe Yes, Maybe No Probable Sure No Way Little Chance As likely as not Good Chance No Doubt Cannot Probably won’t Fifty-fifty Well might Will Will Not Hardly Could Bound To Every Time Vocabulary • Outcome = a possible result in a probability experiment • Sample space = the set of all possible outcomes • Theoretical probability = a comparison of the number of favorable outcomes to the number of possible outcomes (what *should* happen) Theoretical Probability Total sums: _____ Total number of even sums: _____ Total number of odd sums: _____ P (even sum): _____ P (odd sum): _____ 1 1 2 3 4 5 6 2 3 4 5 6 Experimental Probability Rules: Roll both dice Add the 2 numbers Player 1 scores if the sum is even Player 2 scores if the sum is odd Play and tally the sum in the appropriate column Sum Total # of times sum occurred 2 3 4 5 6 7 8 9 10 11 12 Based on your results… Number of even sums rolled: _____ Number of odd sums rolled: ____ Total number of trials: ____ P (odd sum): ____ P (even sum): ____ Rock, Paper, Scissors Predict which player will win the game: A, B, or C? Rules: Player A receives 1 point if all three players display the same hand arrangement Player B receives 1 point if all three players display a different hand arrangement Player C receives 1 point if any two players display the same hand arrangement Theoretical Probability • How many possible outcomes are there? • Player A wins when… – # possible for A vs. total # possible – RRR, PPP, SSS • Player B wins when… – # possible for B vs. total # possible – SRP, SPR, RSP, RPS, PSR, PRS • Player C wins when… – # possible for C vs. total # possible Theoretical Probability • Player A – 3/27 = 11.1% • Player B – 6/27 = 22.2% • Player C – 18/27 = 66.7% Experimental Probability • Play 27 rounds. • Determine (write in your journal) the experimental probability for each player Fair Play? • Decide how many points each player (A, B, and C) should have awarded for winning a turn so that each has an equal chance of winning the game • Explain the reasoning for your choice • Test your plan by playing 27 turns. Record your results and compute the experimental probability of winning for each player. • Evaluate your plan: – Which player won? – Did the changes you made result in a fair chance of winning for each player? – Do you need to make further changes to ensure a fair chance of winning for each player? Explain.