Probability And Statistics Worksheets Page 9
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429-2
Problem Solving Skills:
Simulations
Sometimes a probability problem is too difficult to solve theoretically
Problem Solving
or experimentally. One way to solve such a problem is to model it
Strategies
with a simulation to estimate the probability. Simulations often use
random numbers; these can be readily generated and recorded by a
Guess and check
computer. You can also find random numbers by rolling dice,
Look for a pattern
flipping coins, using numbered slips of paper, or spinning a spinner.
Solve a simpler
problem
P r o b l e m
Make a table, chart
or list
MARKETING
Each box of Batter-Up Pancake Mix contains one of
Use a picture,
5 different classic baseball cards. Assuming that the company has
diagram or model
evenly distributed the cards among the boxes, what is the probability
✔
Act it out
that you will find all 5 cards if you buy 10 boxes of Batter-Up?
Work backwards
Solve the Problem
Eliminate
possibilities
Work with a partner. Use 5 slips of paper numbered 1–5; each slip
Use an equation or
represents a box of cereal. Place the slips in a paper bag. Then draw
formula
one slip of paper from the bag, record its number, and place it back
in the bag. Repeat the process until you have drawn and recorded
10 slips of paper. If you have drawn each of the 5 numbers at least
once, consider the outcome of your experiment to be successful. If
you have not drawn every number, the outcome is unsuccessful.
Repeat the experiment 50 times, recording all results in a table.
Indicate which trials are successful. Then write a ratio comparing
successful outcomes to the total number of outcomes. This ratio
will be an estimate of the probability of getting every card in the set
when you buy 10 boxes of cereal.
T
T
E
RY
HESE
XERCISES
1.
COMPUTER SCIENCE
A computer generates a list of random 2-digit
numbers. Zero cannot be the first digit. What is the probability that a
randomly chosen number from the list contains the digit “1”?
2.
MARKETING
A candy company has placed 6 different prizes in its boxes.
The prizes are uniformly distributed among the boxes of candy, only one per
box. Describe a simulation you could do to estimate the probability of
getting all 6 prizes in a 12-pack of candy.
3.
WRITING MATH
Describe a simulation you could do to find out how many
cards you would expect to have to draw from a standard deck to get two
kings.
4.
TEST TAKING
Suppose you are going to take a 10-question true-false test on
the evolution of idiomatic phrases in Sri Lanka. You will need to guess each
time, and you want to find out your chances of scoring 65% correct or better.
Design a simulation to determine your chances. Hint: Use coin flipping.
388
Chapter 9 Probability and Statistics
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