Download Chapter 4 ntoes - Clinton Public Schools

Statistics Chapter 4
Section 4.1 on Fundamentals of Probability
Name: ____________________________________________ Date: ___________
_______________________ is any process that allows researchers to obtain
observations.
_______________________ is any collection of results or outcomes of an experiment.
_______________________ is an outcome or an event that cannot be broken down any
further.
_______________________for an experiment consists of all possible simple events.
Experiment
Event
Single Event
Sample Spaces
Roll 1 die
Roll 2 dice
Relative Frequency of Probablity/Empirical
P(A) =
Number of times A occurred_____
Number of times experiment was repeated
Classical Approach to Probability
P(A) - number of ways A can occur
Number of different simple events
Law of Large Numbers:
Find the following probabilities:
1. A typical multiple choice question has 5 possible answers. It you make a random
guess on one such question, what is the probability that you are WRONG?
2. Of a sample of deaths compiled by American Casualty Insurance Company, 160
were caused by falls, 120 by poisons, and 70 by fires and burns. If one is selected
randomly, what is the probability is was from poison?
3. Find the probability that a couple with 3 children will have exactly 2 boys
(assume boys and girls are equally likely).
4. A PC World survey of 4000 PCs showed that 992 of them broke down during the
first 2 years. What is the probability of a PC breaking down in the first 2 years?
5. What is the probability that thanksgiving will me on Thursday this year?
___________________ of event A, denoted either A or A, consists of all outcomes in
which event A does NOT occur.
6. If 20 men and 30 women are in a test group, find the probability of NOT getting a
man?
Probabilities should be left in fraction form OR rounded to 3 Significant Digits unless
the decimal is exact.
Section 4.2 Probability Rules
Name: ___________________________________ Date: ____________
Addition Rule
_______________________ is any event combining two or more simple events.
P(A or B) = P(A U B) = P(A) + P(B) – P (A ∩ B)
Events A and B are __________________________ if they cannot occur simultaneously.
Headache
No headache
TOTAL
Seldane
49
732
781
Placebo
49
616
665
Control Group
24
602
626
TOTAL
122
1950
2072
1. If one of the 2072 subjects represented above is randomly selected, find the
probability of getting someone who used a placebo or was in the control group.
2. If one of the 2072 subjects represented above is randomly selected, find the
probability of getting someone who used Seldane or did not experience a
headache.
Multiplication Rule
Two events are _____________________ if one event happening does not influence the
probability of the other event happening.
P(A and B) = P(A) P(B)
3. Choose two cards from a standard deck of 52 with replacement. What is the
probability of choosing a king and then a queen?
Two events are ______________________ if one event happening does influence the
probability of the other event. This is called ___________________ probability.
P(A and B) = P(A) P(B|A)
4. What is the probability of choosing 2 face cards in a row? Assume the cards are
chosen without replacement.
Statistics Chapter 4
Section 4.3 Counting Rules
Name: ________________________________________ Date: ___________
The ______________________________________ states that you can multiply together the
number of possible outcomes for each stage in an experiment in order to obtain the total number
of outcomes for that experiment.
1. Suppose Blake is ordering a banana split with 3 scoops of ice cream. If there are 31
flavors, and he wants al three flavors to be different, how many different ways can his
banana split be made?
2. Robin is preparing a snake for her twins. Matthew and Lainey. She wants to give each
child one item. She has the following snacks on hand: carrots, raisins, crackers, grapes,
applies, yogurt, and granola bars. How many different way cans she prepare a snack for
her twins?
Factorial: The product of all positive integers less than or equal to n.
n! = n (n-1) (n-2)…(2) (1)
0! = 1
Calculate the following
a. 7!
b. 4!
0!
c. 95!
93!
d. 5!
(5 – 3)!
e. 6!
2!(6-2)!
The number of ways of choosing R objects from N distinct objects:
____________________When order is IMPORTANT:
____________________When order is NOT IMPORTANT:
3. A class of 18 fifth graders is holding elections for class president, vice president, and
secretary. How many different ways can the officers be elected?
4. Suppose that baseball coach is putting the 9 starting baseball players in a batting order for
the big game. How many different ways can he order those 9 players?
5. Consider that a cafeteria is serving the following vegetables for lunch one weekday:
carrots, green beans, lima beans, celery, corn, broccoli, and spinach. Suppose now that
Bill wishes to order a vegetable plate with 3 different vegetables. How many ways can
his plate be prepared?
Special Permutations
Some of the objects being counted are identical. Like the letters in MISSISSIPPI
6. How many different ways can you arrange the letters in the word MISSISSIPPI?
7. Tennessee?
8. Maya has a bag of 15 blocks, each of which is a different color including red, blue, and
yellow. Maya reaches into the bag and pulls out 3 blocks. What is the probability that the
blocks she has chosen are red, blue, and yellow?
Practice Problem
9. A homeowner uses the ADT home security system that has a code consisting of 4 digits
(0,1,…..,9) that must be entered in the correct sequence. The digits can be repeated.
a. How many different possibilities are there?
b. If a burglar takes 5 seconds to try each code, how long would it take him to try every
possibility?
10. There are 12 members on the board of directors for the Newport General Hospital.
a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and
secretary, how many different slates of candidates are possible?
b. If they must form an ethics subcommittee of 4 members, how many different
subcommittees are possible?
11. If a couple plans to have 8 children, how many different gender sequences are possible?
12. If a couple has 4 boys and 4 girls, how many different gender sequences are possible?
13. You become suspicious when a genetics researcher randomly selects groups of 20
newborn babies and seems to consistently get 10 girls and 10 boys. The researcher
explains that it is common to get 10 boys and 10 girls in such cases.
a. If 20 newborn babies are randomly selected, how many different gender sequences are
possible?
b. How many different ways can 10 boys and 10 girls be arranged in sequence?
c. What is the probability of getting 10 boys and 10 girls when 20 babies are born?
Based on the preceding results, do you agree with the researcher’s explanation that it is common
to get 10 boys and 10 girls when 20 babies are randomly selected?