Warm Up A tennis tournament with 4 players will be held. In the first round Seed #1 plays Seed #4 and Seed #2 plays Seed #3. The winners meet in the championship.

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Warm Up A tennis tournament with 4 players will be held. In the first round Seed #1 plays Seed #4 and Seed #2 plays Seed #3. The winners meet in the championship. Suppose the following probabilities are known: P(Seed #1 beats Seed #4) = 0.8 P(Seed #1 beats Seed #3) = 0.7 P(Seed #1 beats Seed #2) = 0.6 P(Seed #2 beats Seed #4) = 0.7 P(Seed #2 beats Seed #3) = 0.6 P(Seed #3 beats Seed #4) = 0.6 1) Design a simulation using Table D to estimate the probability of Seed #1 winning the tournament. 2) Run 10 simulations of the tournament. Estimate the probability Seed #1 will win the tournament.

Practice Problems - Round 1 1) List the sample space for flipping a coin 4 times. What is the probability of getting more heads than tails in these 4 flips? 2) What is the probability of rolling 2 dies and getting a double? 3) In a cooler at the picnic there are 5 cans of Coke, 3 cans of Diet Coke, 4 cans of Sprite and 6 cans of Diet Pepsi. If James grabs a can without looking, what is the probability he will get a diet soda? 4) In poker a flush is a hand with 5 cards of the same suit. Assume a player has the 3, 6, 7 and 10 of clubs. If no other cards have been dealt from the deck except these 4, what is the probability the player’s next card will give her a flush?

Practice Problems – Round 2 1) Assume there is a 80% chance of rain for each day of the week (7 day week) and rain on one day doesn’t affect the next day. What is the probability it will rain on every day of the week? 2) Assume a player has the 5, 6, 7 and 8 in a game of poker. If no other cards have been dealt from the deck except these 4, what is the probability the player’s next card will give her a straight (five cards in a row)? 3) Klay Thompson’s 3 point shooting percentage was 44% last year (the probability he will make a three is 0.44). Assume he will shoot 5 threes in a game. What is the probability he will miss at least 1 three in the game?

Practice Problems – Round 3 4) There are 5 nickels, 3 dimes and 7 quarters in a jar. What is the probability of blindly selecting a dime and then a quarter (w/o replacement)? 5) In an AP Stats class 3 of the 19 boys are juniors and 4 of the 14 girls are juniors. What is the probability of randomly selecting a girl or a junior? 6) Alfredo proposes a bet. He says he can get a 6 if he rolls a die 4 times. If he gets a 6 you pay him $10, if he doesn’t get a 6 he pays you $10. Should you take his bet?

Origins of Probability Blaise Pascal and Pierre de Fermat developed the original theories of probability in 1654. This was in response to a request from a French nobleman, the Chevalier de Mere, who was fond of playing a particular dice game. The game consisting of betting if a player could roll double sixes in 24 tries with a pair of dice. The Chevalier believed that betting on double sixes would be profitable but his results indicated otherwise. Which bet is the better option? Why?