Presentation on theme: "PROBABILITY A number 0 to 1 (0% to 100%) that describes how likely an event is to occur."— Presentation transcript:
1PROBABILITYA number 0 to 1 (0% to 100%) that describes how likely an event is to occur.
2Tossing a coin Spinning a spinner Rolling a number cube PROBABILITYTossing a coinSpinning a spinnerRolling a number cube
3The outcome of one event does NOT affect the outcome of the 2nd event. INDEPENDENTThe outcome of one event does NOT affect the outcome of the 2nd event.
4ExamplesBubbette 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
5ExamplesElvis 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)
6Examples AnswersElvis rolls a red die and a blue die. The results of his experiment are recorded (red, blue). What is the P(6, < 3)? 1/18Find P(even, 2) /12Roll a die and flip a coin.Find P(even, heads) 1/4Find P(3, tails) 1/12Find P(7, heads) 0
7ExamplesA 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
13P(event) = number of successes number of trials Experimental probability is what ACTUALLY happens based on repeated trials in an experiment.P(event) = number of successes number of trials
14Experimental Probability Course 310-2Experimental ProbabilityA 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)=
15Course 3The table shows baskets made versus those attempted of 3 NBA players. What is the probability that Shaq will make his next basket?PlayerBaskets madeBaskets AttemptedLeBron James918Kobe Bryant1525Shaquille O’Neal610
17Example 1Decide 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.
18Example 2Decide 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.
19P(historical and then science-fiction) = P(A) · P(B after A) Example 3A 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.58There are 5 historical books out of 8 books.P(historical) =37There are 3 science-fiction books leftout of 7 books.P(science-fiction) =P(historical and then science-fiction) = P(A) · P(B after A)=58371556=Multiply.The probability of Juan choosing a historical book andthen choosing a science-fiction book is1556
20Example 4Alice 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.47P(black) =There are 4 black cards out of 7 cards.36There are 3 red cards left out of 6 cards.P(red) =P(black and then red card) = P(A) · P(B after A)=4736124227=orMultiply.The probability of Alice selecting a black card andthen choosing a red card is .27