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Advanced probability

Thinking Mathematically by Blitzer Sections 11.5 – 11.8. Advanced probability. 11.4 rEVIEW FUNDAMENTALS OF PROBABILITY. Probability. Probability can be expressed as fraction, decimal, or percent!. can be expressed on a scale:. Unlikely. L ikely. P(E) = 50%. P(E) = 0.50. P(E) = 100%.

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Advanced probability

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  1. Thinking Mathematically by Blitzer Sections 11.5 – 11.8 Advanced probability

  2. 11.4 rEVIEWFUNDAMENTALS OF PROBABILITY

  3. Probability Probability can be expressed as fraction, decimal, or percent! • can be expressed on a scale: Unlikely Likely P(E) = 50% P(E) = 0.50 P(E) = 100% P(E) = 0 P(E) = ½ P(E) = 1 Even Chance Impossible Certain

  4. CALCULATING PROBABILITIES The number of results you want The number of possible results The probability of an event happening = This is called the probability of a simple event if there is only one event.

  5. CALCULATING PROBABILITIES The number of results you want The number of possible results The probability of an event happening = THEORETICAL PROBABILITY EX A single die is rolled. Find the probability that the number rolled is a 6.

  6. CALCULATING PROBABILITIES Fair – when the experimental and theoretical probabilities are the same EXPERIMENTAL PROBABILITY THEORETICAL PROBABILITY EX A single die is rolled. Find the probability that the number rolled is a 6. 125646321252 621321445263

  7. CALCULATING PROBABILITIES Can you determine if a die is fair by rolling it only one time? NO NO two times? Fair – when the experimental and theoretical probabilities are the same six times? NO Law of Large Numbers As an experiment is repeated more and more times, the experimental probability of an event gets closer to the theoretical probability of that event (if it is fair).

  8. A Standard Deck of Cards SUITS: Clubs, Diamonds, Hearts SUITS: Clubs, Diamonds, Hearts, Spades Numbers 2 through 10 Jack, Queen, King, Ace SUITS: Clubs, Diamonds Face (Picture) Cards are Jack, Queen, and King SUITS: Clubs • Total of 52 cards • 13 of each suit • 26 red and 26 black • 4 of each number/type • 12 face (picture) cards

  9. Calculating Probabilities EX A single card is drawn at random from a standard deck of cards. What is the probability that the card is red? Probability can be expressed as fraction, decimal , or percent!

  10. Calculating Probabilities EX A single card is drawn at random from a standard deck of cards. What is the probability the card is a red ace?

  11. 11.5Probability with the counting principle,permutations, & combinations

  12. A pizza delivery company offers a deal on one-topping pizzas. There are 3 different crusts to choose from and 9 different toppings. How many different pizzas can be made on this deal?

  13. A pizza delivery company offers a deal on one-topping pizzas. There are 3 different crusts to choose from, and 9 different toppings. A pizza choice is made at random. Find the probability that the pizza has a pan crust and meat topping. Toppings Sausage Pepperoni Onion Mushroom Ham Bacon Green Pepper Black Olives Spinach Crusts Thin Hand-tossed Pan

  14. A restaurant offers 4 appetizers, 6 main courses, 5 drinks, and 2 desserts. How many ways can a meal with each of these be ordered?

  15. A restaurant offers 4 appetizers, 6 main courses, 5 drinks, and 2 desserts. How many ways can a meal with each of these be ordered? chips & salsa spinach dip fried cheese sliders spaghetti steak & potatoes burger & fries chicken tenders chicken fajitas bbq chicken tea Coke Dr. Pepper Sprite Coffee cake pie An order is made at random. What is the probability that the order has chicken and a cola?

  16. Cody bought new t-shirts. He will wear a different shirt for each day of the 5-day school week. How many ways can he wear 5 shirts in the week? If he chooses his shirts at random, what is the probability that he will choose his week’s shirts with a black shirt for Monday and Friday? ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

  17. Callie has 4 apples and 5 oranges. She would like to arrange them in a tray like this: Her brother randomly chooses fruit and places them on the tray. What is the probability that the arrangement turns out the way she wanted it? ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ How many total ways can the fruit be placed in the tray? How many ways can the fruit be placed in the tray as she wants it? total want

  18. There are 20 students in a club. In how many ways can a committee of 4 students be chosen? 4,845 On graphing calculator: 20 MATH PRB nCr ENTER 4 ENTER A combination is an arrangement in which order does NOT matter. The number of possible combinations of r items taken from n items is Combinations… Review

  19. There are 8 male and 10 female students in a club. In how many ways can a committee of 3 be chosen? 816 In how many ways can a committee of 2 females and 1 male be chosen from the students in this club? 45 8 If 3 students are chosen at random from this club, what is the probability a committee of 2 females and 1 male would be chosen? = 45 8 = 360

  20. Calculating Probabilities EX Consider a standard deck and a 5-card poker hand. Find the probability that a flush (all cards of same suit) with hearts is the hand when the cards are dealt randomly. How many ways can get a 5-card hand from only hearts?

  21. Calculating Probabilities EX Consider a standard deck and a 5-card poker hand. Find the probability that a flush (all cards of same suit) with hearts is the hand when the cards are dealt randomly. How many ways can get a 5-card hand from the deck?

  22. Calculating Probabilities EX Consider a standard deck and a 5-card poker hand. Find the probability that a flush (all cards of same suit) with hearts is the hand when the cards are dealt randomly. Write it THIS way…

  23. HOMEWORK 11.5 pg 591 # 1 – 17 odd

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