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MAT 155 Lab 3
Sections 3.6-4.3 Simulation, Counting, Binomial Probability
Page 1 of 3
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Lab3SimCountBinProb
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1.
Use the random digits in the table to the right for developing a simulation for finding the
probability of getting at least four girls in a family of five children. The simulation is to
chose the first ten rows and let the odd digits represent a girl. Complete the table below
and estimate the probability of at least four girls based on your results. How does the
result compare to the correct result of 0.1875?
Row
# girls
2.
3.
1
2
3
4
5
6
7
8
9
10
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Calculate the following and SHOW work in formula.
(a) 7P3 =
(b) 5C2 =
(d) 4! =
(d)
10!
=
7!
Of 9 people, (a) you select a committee of 3, and (b) you elect 3 officers (president, vice-president, and
secretary/treasurer). SHOW your work for each calculation.
(a) How many different 3-person committees are possible?
(b) How many different slates of candidates for officers are possible?
Digits
11079
72196
66732
44201
83443
07356
24826
69526
92645
92948
11632
45801
42884
58830
MAT 155 Lab 3
Sections 3.6-4.3 Simulation, Counting, Binomial Probability
4.
Does P(x) = x/5 (where x can take on the values of 0, 1, 2, 3) describe a probability distribution? Fill in the
table below using fractions for P(x). Explain your answer.
x
5.
P(x)
To settle a paternity suit, two different people are given blood tests. If x is the number having group A blood,
then x can be 0, 1, or 2, and the corresponding probabilities are 0.35, 0.48, and 0.17, respectively (based on
data from the Greater New York Blood Program). Fill in the table below. Determine whether the above
information describes a probability distribution. If it does not, explain why. If it does, find its mean.
x
6.
Page 2 of 3
P(x)
Go to http://cfcc.edu/faculty/cmoore, click on MAT 155, click on Technology, and click on Expected Value
(xls). Enter the numbers from the problem below, type your name below the expected value in the Results,
and print one page in landscape format. When you give a casino $5 for a bet on the “pass line” in the game
of craps, there is a 244/495 probability that you will win $5 and a 251/495 probability that you will lose $5.
What is your expected value? Write one or more sentences to explain your answer.
From the computer Results, the expected value is _______________.
MAT 155 Lab 3
Sections 3.6-4.3 Simulation, Counting, Binomial Probability
Page 3 of 3
7.
Go to http://cfcc.edu/faculty/cmoore, click on MAT 155, click on Technology, click on Probability Distribution
(xls), and click on the ProbDist-Mean-StdDev tab. Enter the data from Problem 8 on page 204, type your
name Cell E2, and print one page in landscape format. Is this a probability distribution? If not, explain why it
is not a probability distribution.
8.
Use the Binomial Probability Formula to find the probability of 4 successes in 7 trials when the probability of
success is 0.2. Show your work and do not round off your answer.
9.
Use the calculator function “binomcdf(” to find the probability of at most 4 successes in 7 trials when the
probability of success is 0.2. Write down what you entered into your calculator and the answer. Do not round
off your answer.
10. Use StatDisk to answer the following questions for a binomial probability distribution when n = 5 and p = 0.4.
Round off your answers to 5-decimal places.
(a) P(x = 3) =
(b) P(x ≤ 4) =
(c) P(x ≥ 2) =
(d) P(x < 2) =
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