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 Virginia’s 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 ∙26 ∙26 ∙10 ∙10 ∙10 ∙10=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.

𝑃 (𝑎𝑡 𝑙𝑒𝑎𝑠𝑡10 )=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 cousin’s telephone number?

18 ∙10 ∙10 ∙10 ∙10 ∙10 ∙10

=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.

𝑃 (𝑒𝑣𝑒𝑛𝑜𝑟𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛6 )=𝑃 (𝑒𝑣𝑒𝑛)+𝑃 (𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛6 )−𝑃 (𝑒𝑣𝑒𝑛𝑎𝑛𝑑𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛6 )=48+28−18=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.).

· Of all students who received one or more plus grades, 92% were undergraduates and 8% were graduates.

· 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

𝑃 ¿

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?

𝑃 (𝑐𝑜𝑟𝑟𝑒𝑐𝑡 h𝑡𝑜𝑜𝑡 𝑝𝑎𝑠𝑡𝑒𝑎𝑛𝑑𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑑𝑒𝑛𝑡𝑎𝑙𝑟𝑖𝑛𝑠𝑒 )=𝑃 (𝑐𝑜𝑟𝑟𝑒𝑐𝑡 h𝑡𝑜𝑜𝑡 𝑝𝑎𝑠𝑡𝑒 ) ∙𝑃 (𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑑𝑒𝑛𝑡𝑎𝑙𝑟𝑖𝑛𝑠𝑒 )=18∙15=140≈ 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.

𝑃 (𝑐𝑎𝑟𝑑𝑖𝑠 𝑎 4 h𝑡 𝑟𝑢8𝑜𝑟 𝑎𝑐𝑙𝑢𝑏 )=𝑃 (𝑐𝑎𝑟𝑑𝑖𝑠 4 h𝑡 𝑟𝑢8 )+𝑃 (𝑐𝑎𝑟𝑑𝑖𝑠 𝑎𝑐𝑙𝑢𝑏 )−𝑃 (𝑐𝑎𝑟𝑑 𝑖𝑠 4 h𝑡 𝑟𝑢8𝑎𝑛𝑑 𝑎𝑐𝑙𝑢𝑏 )=2052

+1352−552

=2852≈0.538

What is our clue? or

Which rule will we use? Addition rule

Are the events mutually exclusive? no

Permutations

𝑛 !(𝑛−𝑟 )!

Combinations

𝑛!(𝑛−𝑟 )! ∙𝑟 !

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.

𝑃 (𝑁𝑢𝑟𝑠𝑖𝑛𝑔𝑚𝑎𝑗𝑜𝑟 )= 7953537

≈0.225

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.

𝑃 (𝑚𝑎𝑙𝑒)=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.

𝑃 (𝑁𝑢𝑟𝑠𝑖𝑛𝑔𝑚𝑎𝑗𝑜𝑟|𝑚𝑎𝑙𝑒 )= 951110

≈0.086

A printing company’s 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.

𝑃 (𝑛𝑜𝑡𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒 )=1−0.005=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.

𝑃 (𝑑𝑖𝑎𝑚𝑜𝑛𝑑𝑜𝑟 7 )=𝑃 (𝑑𝑖𝑎𝑚𝑜𝑛𝑑 )+𝑃 (7 )−𝑃 (𝑑𝑖𝑎𝑚𝑜𝑛𝑑𝑎𝑛𝑑7 )=1352

+452−152

=1652≈0.308

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.

𝑃 (𝑟𝑒𝑑𝑜𝑟𝑞𝑢𝑒𝑒𝑛 )=𝑃 (𝑟𝑒𝑑 )+𝑃 (𝑞𝑢𝑒𝑒𝑛)−𝑃 (𝑟𝑒𝑑𝑎𝑛𝑑𝑞𝑢𝑒𝑒𝑛 )=2652

+452−252≈ 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.

𝑃 (3𝑜𝑟 𝑓𝑎𝑐𝑒𝑐𝑎𝑟𝑑 )=𝑃 (3 )+𝑃 ( 𝑓𝑎𝑐𝑒𝑐𝑎𝑟𝑑 )= 452

+1252≈0.308

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.

𝑃 (6𝑜𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛 4 )=𝑃 (6 )+𝑃 (𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛4 )−𝑃 (6𝑎𝑛𝑑𝑔𝑟𝑒𝑎𝑡𝑒𝑟 h𝑡 𝑎𝑛 4 )=16+26−16=26≈ 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.

𝑃 (𝑙𝑒𝑠𝑠 h𝑡 𝑎𝑛5𝑜𝑟 𝑜𝑑𝑑 )=𝑃 (𝑙𝑒𝑠𝑠 h𝑡 𝑎𝑛5 )+𝑃 (𝑜𝑑𝑑 )−𝑃 (𝑙𝑒𝑠𝑠 h𝑡 𝑎𝑛5 𝑎𝑛𝑑𝑜𝑑𝑑 )=46+36−26=56≈0.833

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.

𝑃 (3𝑜𝑟𝑒𝑣𝑒𝑛 )=𝑃 (3 )+𝑃 (𝑒𝑣𝑒𝑛)=16+36≈0.667

What is our clue? or

Which rule will we use? Addition rule

Are the events mutually exclusive? yes