Simulations

1. Section 5.1 in your book…

2.  A simulation is an imitation of chance
behavior, most often carried out with random
numbers.

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.  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.  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.  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.  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.  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.  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.  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.  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.