Transcript 10-3 Use a Simulation

10-3 Use a Simulation
Warm Up
Problem of the Day
Lesson Presentation
Course 3
10-3 Use a Simulation
Warm Up
1. There are 25 out of 216 sophomores enrolled in
a physical-education course. Estimate the
probability that a randomly selected sophomore
is enrolled in a physical-education course.
0.12
2. A spinner was spun 230 times. It landed on red
120 times, green 65 times, and yellow 45 times.
Estimate the probability of its landing on red.
0.52
Course 3
10-3 Use a Simulation
Problem of the Day
If a triangle is worth 7 and a rectangle
is worth 8, how much is a hexagon
worth?
10
Course 3
10-3 Use a Simulation
Learn to use a simulation to estimate
probability.
Course 3
10-3 Use
Insert
Lesson Title Here
a Simulation
Vocabulary
simulation
random numbers
Course 3
10-3 Use a Simulation
A simulation is a model of a real
situation. In a set of random numbers,
each number has the same probability of
occurring as every other number, and no
pattern can be used to predict the next
number. Random numbers can be used to
simulate random events in real situations.
Course 3
10-3 Use a Simulation
Additional Example 1: Problem Solving Application
A dart player hits the bull’s-eye 25%
of the times that he throws a dart.
Estimate the probability that he will
make at least 2 bull’s-eyes out of his
next 5 throws.
1
Understand the Problem
The answer will be the probability that he
will make at least 2 bull’s-eyes out of his next
5 throws.
List the important information:
• The probability that the player will hit the
bull’s-eye is 0.25.
Course 3
10-3 Use a Simulation
Additional Example 1 Continued
2
Make a Plan
Use a simulation to model the situation.
Use digits grouped in pairs. The numbers 01–
25 represent a bull’s-eye, and the numbers
26–00 represent an unsuccessful attempt.
Each group of 10 digits represent one trial.
Course 3
10-3 Use a Simulation
Additional Example 1 Continued
3
Solve
Starting on the
third row of the
table of p. 532 and
using 10 digits for
each trial yields
the data at right:
Course 3
10-3 Use a Simulation
Additional Example 1 Continued
Helpful Hint
Calculators and computers can generate
sets of approximately random numbers.
A formula is used to generate the
numbers, so they are not truly random,
but they work for most simulations.
Course 3
10-3 Use a Simulation
Additional Example 1 Continued
Out of the 10 trials, 2 trials represented two or
more bull’s-eyes. Based on this simulation, the
probability of making at least 2 bull’s-eyes out
of his next 5 throws is about 2 , or 20%.
10
4
Look Back
Hitting the bull’s-eye at a rate of 20% means
the player hits about 20 bull’s-eye out of every
100 throws. This ratio is equivalent to 2 out of
10 throws, so he should make at least 2 bull’seyes most of the time. The answer is
reasonable.
Course 3
10-3 Use a Simulation
Check It Out: Example 1
Tuan wins a toy from the toy grab machine
at the arcade 30% of the time. Estimate the
probability that he will win a toy 1 time out
of the next 3 times he plays.
1
Understand the Problem
The answer will be the probability that he
will win 1 of the next 3 times.
List the important information:
• The probability that Tuan will win is 30%.
Course 3
10-3 Use a Simulation
Check It Out: Example 1 Continued
2
Make a Plan
Use a simulation to model the situation. Use
digits grouped in pairs. The numbers 01–30
represent a win, and the numbers 31–00
represent an unsuccessful attempt. Each
group of 6 digits represent one trial.
Course 3
10-3 Use a Simulation
Check It Out: Example 1 Continued
3
Solve
Starting on the
fourth row of
the table on p.
532 and using
6 digits for
each trial yields
the data at
right:
Course 3
86 58 52
79 19 65 1 win
26 49 35 1 win
57 94 42
51 33 25
16 63 52 1 win
85 84 18 1 win
39 47 32
66 67 89
93 87 83
10-3 Use a Simulation
Check It Out: Example 1 Continued
Out of the 10 trials, 4 trials represented one
or more wins. Based on this simulation, the
probability of winning at least 1 time out of
his next 3 games is 40%
4
Look Back
Winning at a rate of 40% means that Tuan
wins about 40 times out of every 100 games.
This ratio is equivalent to 4 out of 10 games,
so he should win at least 4 toys most of the
time. The answer is reasonable.
Course 3
10-3 Use
Insert
a Simulation
Lesson Title Here
Lesson Quiz
Use the table of random numbers to simulate
the situation.
38094
76211
43659
29272
76005
93391
19587
47380
33442
40809
27904
95412
69632
48461
25654
55889
69632
48461
25654
55889
42231
39983
13802
24483
52730
15604
80949
46351
10580
59765
76431
38586
62987
40440
93594
30198
64926
17672
68735
35168
19085
35497
30798
21966
Course 3
Lydia gets a hit 34% of
the time she bats.
Estimate the probability
that she will get at least
4 hits in her next 10 at
bats.
Possible answer: 30%