probability and statistics chapter 3 review. identify the sample space of the probability experiment...
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Probability and StatisticsChapter 3 Review
Identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram.
Probability experiment: Guessing the gender of the three children in a family
Event: The family has two boys
The state of Virginiaβs license plate has three letters followed by four digits. Assuming that any letter or digit can be use, how many different license plates are possible?
Use the Fundamental Counting Principle
26 β26 β26 β10 β10 β10 β10=175,760,000
Number of Employees 0 to 4 5 to 9 10 to 19 20 to 99 100 or
more
Percent of Firms 60.8% 17.7% 10.8% 8.9% 1.8%
The table below shows the approximate distribution of the sizes of firms for 2004. Use the table to determine what is the probability that a randomly selected firm will have at least 10 employees?
Change the percentages to decimals.
π (ππ‘ ππππ π‘10 )=0.108+0.089+0.018=0.215
The telephone numbers for a region of a state have an area code of 570. The next seven digits represent the local telephone numbers for that region. A local telephone number can not begin with a 0 or 1. Your cousin lives within the given area code. What is the probability of randomly generating your cousinβs telephone number?
18 β10 β10 β10 β10 β10 β10
=1
8000000
An eight sided die, numbered 1 thru 8, is rolled. Find the probability that the roll results in an even number or a number greater than 6.
π (ππ£πππππππππ‘ππ hπ‘ ππ6 )=π (ππ£ππ)+π (πππππ‘ππ hπ‘ ππ6 )βπ (ππ£ππππππππππ‘ππ hπ‘ ππ6 )=48+28β18=58=0.625
What is our clue word? or
Which rule will we use? The addition rule
Are the events mutually exclusive? No
The list below shows the results of a study on the use of plus/ minus grading at North Carolina State University. It shows the percents of graduates and undergraduate students who received grades with pluses and minuses (for example C+, A-, etc.).
Β· Of all students who received one or more plus grades, 92% were undergraduates and 8% were graduates.
Β· Of all students who received one or more minus grades, 93% were undergraduate and 7% were graduates.
Find the probability that a student is an undergraduate student, given that the student received a plus grade.
What is our clue? given that Conditional probability
π ΒΏ
You are shopping and your roommate has asked you to pick up toothpaste and dental rinse. However, your roommate did not tell you which brands to get. The store has a eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both products?
π (πππππππ‘ hπ‘πππ‘ πππ π‘πππππππππππ‘ ππππ‘ππππππ π )=π (πππππππ‘ hπ‘πππ‘ πππ π‘π ) βπ (πππππππ‘ ππππ‘ππππππ π )=18β15=140β 0.025
What is our clue? and
Which rule will we use?
Are they dependent or independent events?
Multiplication rule
independent
A card is randomly selected from the standard deck. Find the probability that the card is between 4 and 8 (inclusive) or is a club.
π (ππππππ π 4 hπ‘ ππ’8ππ ππππ’π )=π (ππππππ 4 hπ‘ ππ’8 )+π (ππππππ ππππ’π )βπ (ππππ ππ 4 hπ‘ ππ’8πππ ππππ’π )=2052
+1352β552
=2852β0.538
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? no
Permutations
π !(πβπ )!
Combinations
π!(πβπ )! βπ !
The table shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Sciences Center for a recent semester.
π (ππ’ππ ππππππππ )= 7953537
β0.225
The table shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Sciences Center for a recent semester.
π (ππππ)=11103537
=0.314
The table shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Sciences Center for a recent semester.
π (ππ’ππ ππππππππ|ππππ )= 951110
β0.086
A printing companyβs bookbinding machine has a probability of 0.005 of producing a defective book. This machine is used to bind three books. Find the probability that none of the books is defective.
π (πππ‘ππππππ‘ππ£π )=1β0.005=0.995
Which rule will we use? Multiplication rule
A card is selected at random from a standard deck. Find the probability of selecting a diamond or a 7.
π (πππππππππ 7 )=π (πππππππ )+π (7 )βπ (ππππππππππ7 )=1352
+452β152
=1652β0.308
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? no
A card is selected at random from a standard deck. Find the probability of selecting a red suit or a queen.
π (πππππππ’πππ )=π (πππ )+π (ππ’πππ)βπ (ππππππππ’πππ )=2652
+452β252β 0.538
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? No
A card is selected at random from a standard deck. Find the probability of selecting a 3 or a face card.
π (3ππ ππππππππ )=π (3 )+π ( ππππππππ )= 452
+1252β0.308
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? yes
You roll a die. Find the probability of rolling a six or a number greater than four.
π (6ππ πππππ‘ππ hπ‘ ππ 4 )=π (6 )+π (πππππ‘ππ hπ‘ ππ4 )βπ (6ππππππππ‘ππ hπ‘ ππ 4 )=16+26β16=26β 0.333
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? no
You roll a die. Find the probability of rolling a number less than five or an odd number.
π (πππ π hπ‘ ππ5ππ πππ )=π (πππ π hπ‘ ππ5 )+π (πππ )βπ (πππ π hπ‘ ππ5 ππππππ )=46+36β26=56β0.833
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? no
You roll a die. Find the probability of rolling a three or an even number.
π (3ππππ£ππ )=π (3 )+π (ππ£ππ)=16+36β0.667
What is our clue? or
Which rule will we use? Addition rule
Are the events mutually exclusive? yes