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Math 116 – Introduction to Chapter 4
Due next class (2, 3-a,b,c)
Name_________________
1) Consider the experiment of “tossing a coin three times and counting
the number of heads”.
(a) Develop the sample space of the experiment by using a tree
diagram
(b) Construct a frequency distribution.
(c) Construct a frequency histogram.
(d) Construct a probability distribution.
(e) Construct a probability histogram.
(f) If we toss a coin three times, what is the “theoretical” probability
of getting exactly 2 heads?
(g) Find P(x  2)
2) Simulation
*** Now we’ll simulate the experiment of “tossing a coin three times” and
counting the number of heads”.
Let
1 = Head
2 = Tail
Use your calculator to generate three random integers from 1 to 2 by doing
MATH
PRB
5:randInt(1,2,3)
ENTER
(this is one repetition of the experiment)
Repeat the experiment 25 times and record information in the table.
(keep pressing ENTER 24 more times and tally results below)
#head
s
0
1
2
3
tally frequenc
y
(a) If we toss a coin three times, what is the “experimental” probability
of getting exactly 2 heads?
(compare with (f) in previous
page)
(b) Find P(x  2)
(compare with (g) in previous page)
 Law of Large Numbers
As we repeat an experiment a large number of times, the “experimental”
probability gets closer to the “theoretical” probability.
3) Consider the experiment of “having four children and counting the
number of girls”
a) Develop the sample space of the experiment by using a tree
diagram
b) Construct a frequency distribution.
c) Construct a frequency histogram.
d) Construct a probability distribution
e) Construct a probability histogram
f) What is the “theoretical” probability of having exactly 3 girls?
g) Find P(x  3)
h) Simulate the experiment repeating 20 times
i) Answer (f) and (g) again to find the “experimental”
probabilities and compare answers.