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PROBABILITY

PROBABILITY. A number 0 to 1 (0% to 100%) that describes how likely an event is to occur. PROBABILITY. Tossing a coin Spinning a spinner Rolling a number cube. INDEPENDENT. The outcome of one event does NOT affect the outcome of the 2 nd event. Examples.

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PROBABILITY

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  1. PROBABILITY A number 0 to 1 (0% to 100%) that describes how likely an event is to occur.

  2. PROBABILITY Tossing a coin Spinning a spinner Rolling a number cube

  3. INDEPENDENT • The outcome of one event does NOT affect the outcome of the 2nd event.

  4. Examples • Bubbette has three quarters and five dimes in her pocket. She takes out one coin, then places it back in her pocket. Then she draws a second coin. What is the probability of drawing a dime and then a quarter? [P(dime and quarter)] • Answer 15/64

  5. Examples • Elvis rolls a red die and a blue die. The results of his experiment are recorded (red, blue). What is the P(6, < 3)? • Find P(even, 2) • Roll a die and flip a coin. Find P(even, heads) • Find P(3, tails) • Find P(7, heads)

  6. Examples Answers • Elvis rolls a red die and a blue die. The results of his experiment are recorded (red, blue). What is the P(6, < 3)? 1/18 • Find P(even, 2) 1/12 • Roll a die and flip a coin. • Find P(even, heads) 1/4 • Find P(3, tails) 1/12 • Find P(7, heads) 0

  7. Examples • A bag contains red and white buttons. Suppose you choose a button, replace it, and choose another button. The probability of choosing a red, then a white button is 3/10. If the probability of choosing a red button is 3/5, what is the probability of choosing a white button? • Answer 1/2

  8. THEORETICAL PROBABILITY

  9. Theoretical probability is based on what we EXPECT to happen. P(event) = Number of favorable outcomes Total number of outcomes

  10. Course 3 An experiment consists of spinning this spinner once. Find the probability of each event. • P(4)= • P(odd number) = • P(2 or 3) = • P (6) = • P(integer) =

  11. Course 3 One fair number cube is rolled. Find the probability of the following. • P(4)= • P(even number)= • P(not 6) = • P(7)=

  12. EXPERIMENTAL PROBABILITY

  13. P(event) = number of successes number of trials Experimental probability is what ACTUALLY happens based on repeated trials in an experiment.

  14. Experimental Probability 10-2 Course 3 A marble is randomly drawn out of a bag and then replaced. The table shows the results after fifty draws. • P(red)= • P(green or red)=

  15. Course 3 The table shows baskets made versus those attempted of 3 NBA players. What is the probability that Shaq will make his next basket?

  16. Dependent Probability

  17. Example 1 Decide whether the set of events are dependent or independent. Explain your answer. Kathi draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube. Since the outcome of drawing the card does not affect the outcome of rolling the cube, the events are independent.

  18. Example 2 Decide whether the set of events are dependent or independent. Explain your answer. Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain. Since Janette cannot pick the same book that Yuki picked, and since there are fewer books for Janette to choose from after Yuki chooses, the events are dependent.

  19. 5 8 3 7 · = Example 3 A reading list contains 5 historical books and 3 science-fiction books. What is the probability that Juan will randomly choose a historical book for his first report and a science-fiction book for his second? The first choice changes the number of books left, and may change the number of science-fiction books left, so the events are dependent. 5 8 There are 5 historical books out of 8 books. P(historical) = 3 7 There are 3 science-fiction books left out of 7 books. P(science-fiction) = P(historical and then science-fiction) = P(A) · P(B after A) 15 56 = Multiply. The probability of Juan choosing a historical book and then choosing a science-fiction book is 15 56 ·

  20. 4 7 3 6 · = Example 4 Alice was dealt a hand of cards consisting of 4 black and 3 red cards. Without seeing the cards, what is the probability that the first card will be black and the second card will be red? The first choice changes the total number of cards left, and may change the number of red cards left, so the events are dependent. 4 7 P(black) = There are 4 black cards out of 7 cards. There are 3 red cards left out of 6 cards. 3 6 P(red) = P(black and then red card) = P(A) · P(B after A) 2 7 12 42 or Multiply. = The probability of Alice selecting a black card and then choosing a red card is . 2 7

  21. Problems 12 and 13 do NOT have a correct answer. Cross out the choices.

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