Download LAB 4

MATH1342
Collin College
LAB 4
Spring 2015
NAME: _________________
Instructor: Daryl Rupp
DUE DATE: WE - 2/16/15
SCC - 2/17/15
PART I:
1. Given a single die with FOUR sides (instead of 6 – NOT 6 sides) where each side will have
a number: one side numbered 1, one side numbered 2, one side numbered 3 and one side
numbered 4. The die will be made of hard rubber so it will bounce before coming to rest.
The number on the side that lands “down” will be the outcome.
a. What will be the sample space of the experiment of rolling one die?
b. What is P(3)? ________ P(5)? ____
P(even number)? ________
P(1  x  4 )? ______
P(x < 4)? _______
c. Now consider the experiment of rolling 2 of the four sided dice and the outcome is the total
of the two “down” sides. The sample space will be {2, 3, 4, 5, 6, 7, 8}. Find in the number
of ways each of the sample space outcomes can be obtained and fill in the table below
including the probability of each outcome and the total of all probabilities:
Outcome
2
3
4
5
6
7
8
Total
# of Ways
P(Outcome)
d. In problem 1c. above, if one event is rolling a 6 and another event is rolling an 8, then are
these two events
Mutually Exclusive
or
Not Mutually Exclusive
PART II:
Some plain M&M’s and some peanut M&M’s are mixed in a bag. The following is the number of
each color and type of M&M found in the bag of 360 M&M’s. Use the table for Part II and Part
III.
Red
Orange
Yellow
Green
Blue
Brown
TOTAL
Plain Peanut Total
50
35
15
75
52
23
72
50
22
51
35
16
33
23
10
79
55
24
250
110
360
Suppose you reach into the bag and randomly select one M&M. Calculate the following
probabilities of selecting one M&M that is (described). Show your calculations and round your
answers to 4 decimals.
1. P (Red) =
2. P (Peanut) =
3. P (Blue) =
4. P (Blue and Plain) =
5. P (Orange and Brown) =
6. P(Orange or Brown) =
7. P (Not Yellow) =
8. P (Blue or Plain) =
9. P (Brown give that the one you picked is Plain) =
PART III:
Use the same table of data from Part II.
Suppose you reach into the sample bag and randomly select THREE M&M’s.
Calculate the following probabilities (with and without replacement).
Show your calculations and round your final answers to 4 decimals.
1. The probability that the first M&M is Red, the second M&M is Yellow, and the third M&M is
Blue.
(with replacement)
2. The probability that the first M&M is Red, the second M&M is Yellow, and the third M&M is
Blue.
(without replacement)
3. The probability that all three M&M’s are Blue.
(with replacement)
4. The probability that all three M&M’s are Blue.
(without replacement)
5. Would it be unusual for all three M&M’s to be blue if the sampling is done without
replacement?
Justify your answer using a complete sentence and proper grammar.
PART IV:
The following problems use the counting techniques methods used in Section 5.5. Show your
calculations and the answers will be in whole numbers.
1. If a three character code is to be made from the letters {a, b, c, d, e} and the letters can be
reused, how many different codes can be made?
2. Same as 1. without reusing any letter?
3. If you are selecting a meal from a menu and you have 4 choices of appetizers, 2 choices of
salads, 5 choices of main courses, 6 choices of desserts, how many different meals do you
have to select from (assuming you had to have one selection from each course)?
4. Given that 52% of a city (of more than 1,000,000 people) are in favor of a bond issue and 4
people who favored it are to be selected from the voters in the city, what is the probability
that the first 4 people selected would favor the issue?
5. A lottery consists of selecting 3 single digits from the 10 digits (0 through 9), without
replacement and order matter. How many different 3 digit numbers can be made?
6. A lottery consists of selecting 3 single digits from the 10 digits (0 through 9), without
replacement and order does not matter. How many different 3 digit numbers can be made?