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# Simulations

Simulations

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### Simulations

1. 1. Section 5.1 in your book…
2. 2.  A simulation is an imitation of chance behavior, most often carried out with random numbers.
3. 3.  Rolling a Die  Flipping a Coin  Random Number Table (refer to as Table D)  RandInt (on the calculator)  The command is RandInt(first,last,times)  Pulling a card (or cards) from a deck of cards
4. 4.  A couple wants to have a boy to carry on the family name. If they keep having children until they get a boy what is the probability that they will have boy before they have five children?  Assign H – boy and T – girl  Flip a coin 5 times and record your results  Do this experiment 20 times and record
5. 5.  On average, how many children did the couple have before they had a boy? ◦ If your result was GGBGB you would label that result line as 3 because the third child was a boy. ◦ Average your 20 lines. ◦ Come and list your averages: ◦ Class average:
6. 6.  Go to page 290 and read the green box with “Golden Ticket Parking Lottery”  What is the probability that a fair lottery would result in 2 winners from the same class?  Use Table D ◦ Label AP students O1-28 ◦ Label all other students 29-95
7. 7.  There are 4 marbles in a bag (blue, red, green, yellow). What is the probability that you choose a yellow marble?  If you are assigning students to 6 groups in a class, what is the probability that a group ends up with all members being girls?  You have a choice of 3 colleges to attend. If you wanted to randomly choose, what is the probability that you chose the one that was in state?
8. 8.  Each box of cereal contains 1 collectible card. There are 5 different collectible cards available, each with a different driver.  Each of the 5 cards are equally likely to be in your cereal box.  What is the probability that it will take 23 or more boxes to get a full set of 5 NASCAR collectible cards?
9. 9.  Label 1 – Jeff Gordon  Label 2 – Dale Earnhardt, Jr  Label 3 – Tony Stewart  Label 4 – Danica Patrick  Label 5 – Jimmie Johnson  RandInt(1,5) simulates buying one box of cereal and looking at the card.  Since we want a full set of cards, we will keep pressing enter until we get all five labels from 1-5 and record how many times it took.
10. 10.  Do this 10 times and record how many boxes it took you each time.  Did anyone have to buy more than 22 boxes before you got all 5 cards?  The probability that it will take 23 boxes of cereal before collecting all 5 cards is roughly 0.
11. 11.  State: What is the question of interest about some chance process?  Plan: Describe how to use a chance device to imitate one repetition of the process. Explain clearly how to identify the outcomes of the chance process and what variable to measure.  Do: Perform many repetitions of the simulation.  Conclude: Use the result of our simulation to answer the question of interest.