1308 SIP Activity 3-Analysis of Coin Spins-AOP jonathan
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Tarrant County College South East *
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Course
1308
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by GeneralSnailPerson940
Name:
MATH 1308-088
Groupmates: _________________________________________________________________________
Single Coin Tosses
Coin Toss Trials (Part 1)
In this activity, each groupmate
will either toss (spin) a coin or
access the StatCrunch applet* to
produce at least 3 trials of 10 tosses each
. * StatCrunch applet is found via QUICK LINKS > MyLab StatCrunch > StatCrunch website > Interactive applets > Simulations > “Probability of a head with a fair coin.” Flip only 1 coin at a time
and record results
for 10 flips. Record your results and the results of your groupmates in the table below. As a group
, record at least 12 trials of 10 tosses each.
The exact sequence of heads and tails should be written in the Outcomes column. Trial #
Contributor
Name
Outcomes (Head or Tail)
No. of Heads
1
T
H
H
H
H
H
T
T
T
H
6
2
T
H
H
H
H
T
T
H
H
T
6
3
T
T
T
T
H
H
T
T
H
H
4
4
5
6
7
8
9
10
11
12
After all data from the group are collected
, make a histogram of the ‘Frequency of trials resulting in 16
number of heads
,’ i.e., the frequency with which a certain number of heads occurred: 0 time, 1 time, 2 times, 3 times, … etc., among your 12 trials. The histogram can be created with StatCrunch, Excel, or on the graphing paper provided on the next page. If using graphing paper, use 2 squares for each bar width. If using software, add
additional sheets to insert graphs as needed.
Name:
MATH 1308-088
Groupmates: _________________________________________________________________________
Name:
MATH 1308-088
Groupmates: _________________________________________________________________________
Theoretical Analysis (Part 2)
*Complete the table below, including all remaining theoretical probabilities. Enter the results from your group’s actual trials in the last two columns. (
Ex
: the empirical probability
of obtaining exactly 4 heads in 10 tosses is the proportion
of your twelve trials that resulted in obtaining 4 heads.)
No. of
heads
No. of
combinations
Probability
of an
individual
outcome
Theoretical Probability
Frequency
of trials
with this
No. of
heads
Empirical
Probability
of this No.
of heads
0
10
!
0
!
(
10
−
0
)
!
=
1
1
2
1
×
(
1
2
)
0
×
(
1
−
1
2
)
10
=
0.001
1/16
0
1
10
!
1
!
(
10
−
1
)
!
=
10
1
2
10
×
(
1
2
)
1
×
(
1
−
1
2
)
9
=
0.01
1/10
.1
2
10
!
2
!
(
10
−
2
)
!
=
45
1
2
45
(
1
2
)
2
(
1
−
1
2
)
8
=
0.044
1/5
.2
3
10
!
3
!
(
10
−
3
)
!
=
120
1
2
120
(
1
2
)
3
(
1
−
1
2
)
7
=
0.117
3/10
.3
4
10
!
4
!
(
10
−
4
)
!
=
210
½
210
(
1
2
)
4
(
1
−
1
2
)
6
=
¿
.205
2/5
.4
5
10
!
5
!
(
10
−
5
)
!
=
252
½
252
(
1
2
)
5
(
1
−
1
2
)
5
=
¿
.246
1/2
.5
6
10
!
6
!
(
10
−
6
)
!
=
¿
2
10
½
210
(
1
2
)
6
(
1
−
1
2
)
4
=
.205
3/5
.6
7
10
!
7
!
(
10
−
7
)
!
=
120
½
120
(
1
2
)
7
(
1
−
1
2
)
3
=
¿
.117
7/10
.7
8
10
!
8
!
(
10
−
8
)
!
=
¿
4
5
½
45
(
1
2
)
8
(
1
−
1
2
)
2
=
¿
.044
4/5
.8
9
10
!
9
!
(
10
−
9
)
!
=
¿
1
0
½
10
(
1
2
)
9
(
1
−
1
2
)
1
=
.0097
9/10
.9
10
10
!
10
!
(
10
−
10
)
!
=
1
½
1
(
1
2
)
10
(
1
−
1
2
)
0
=
¿
.00097
1/1
.10
*Hint: Use StatCrunch > Stat > Calculators > Binomial to quickly calculate the Theoretical Probabilities.
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Name:
MATH 1308-088
Groupmates: _________________________________________________________________________
1.
(a) What are the theoretical probabilities of obtaining 0 heads, 1 head, 9 heads, and 10 heads?
1.
(b) Are these probabilities considered usual/unusual, why/why not? 2.
What were your group’s empirical probabilities of obtaining 0 heads, 1 head, 9 heads, and 10 heads?
3.
Discuss the differences, if any, between the theoretical and your empirical probabilities. Do differences indicate that the coins were not fair coins? Explain.