Probability and Statistics Chapter 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

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? 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% Change the percentages to decimals. 𝑃 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 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 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? 1 8∙10∙10∙10∙10∙10∙10 = 1 8000000

An eight sided die, numbered 1 thru 8, is rolled 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. What is our clue word? or Which rule will we use? The addition rule Are the events mutually exclusive? No 𝑃 𝑒𝑣𝑒𝑛 𝑜𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 6 =𝑃 𝑒𝑣𝑒𝑛 +𝑃 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 6 −𝑃 𝑒𝑣𝑒𝑛 𝑎𝑛𝑑 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 6 = 4 8 + 2 8 − 1 8 = 5 8 =0.625

𝑃(𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑖𝑠 𝑎𝑛 𝑢𝑛𝑑𝑒𝑟𝑔𝑟𝑎𝑑𝑢𝑎𝑡𝑒|𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑎 𝑝𝑙𝑢𝑠 𝑔𝑟𝑎𝑑𝑒=0.92 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(𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑖𝑠 𝑎𝑛 𝑢𝑛𝑑𝑒𝑟𝑔𝑟𝑎𝑑𝑢𝑎𝑡𝑒|𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑎 𝑝𝑙𝑢𝑠 𝑔𝑟𝑎𝑑𝑒=0.92

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? What is our clue? and Which rule will we use? Multiplication rule Are they dependent or independent events? independent 𝑃 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑡𝑜𝑜𝑡ℎ𝑝𝑎𝑠𝑡𝑒 𝑎𝑛𝑑 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑑𝑒𝑛𝑡𝑎𝑙 𝑟𝑖𝑛𝑠𝑒 =𝑃 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑡𝑜𝑜𝑡ℎ𝑝𝑎𝑠𝑡𝑒 ∙𝑃 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑑𝑒𝑛𝑡𝑎𝑙 𝑟𝑖𝑛𝑠𝑒 = 1 8 ∙ 1 5 = 1 40 ≈0.025

A card is randomly selected from the standard deck 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. What is our clue? or Which rule will we use? Addition rule Are the events mutually exclusive? no 𝑃 𝑐𝑎𝑟𝑑 𝑖𝑠 𝑎 4 𝑡ℎ𝑟𝑢 8 𝑜𝑟 𝑎 𝑐𝑙𝑢𝑏 =𝑃 𝑐𝑎𝑟𝑑 𝑖𝑠 4 𝑡ℎ𝑟𝑢 8 +𝑃 𝑐𝑎𝑟𝑑 𝑖𝑠 𝑎 𝑐𝑙𝑢𝑏 −𝑃 𝑐𝑎𝑟𝑑 𝑖𝑠 4 𝑡ℎ𝑟𝑢 8 𝑎𝑛𝑑 𝑎 𝑐𝑙𝑢𝑏 = 20 52 + 13 52 − 5 52 = 28 52 ≈0.538

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 𝑁𝑢𝑟𝑠𝑖𝑛𝑔 𝑚𝑎𝑗𝑜𝑟 = 795 3537 ≈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 = 1110 3537 =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 𝑁𝑢𝑟𝑠𝑖𝑛𝑔 𝑚𝑎𝑗𝑜𝑟 𝑚𝑎𝑙𝑒 = 95 1110 ≈0.086

A printing company’s bookbinding machine has a probability of 0 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 𝑛𝑜𝑡 𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒 =1−0.005=0.995 Which rule will we use? Multiplication rule 𝑃 𝑛𝑜𝑡 𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ∙𝑃 𝑛𝑜𝑡 𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒 ∙𝑃 𝑛𝑜𝑡 𝑑𝑒𝑓𝑒𝑐𝑡𝑖𝑣𝑒 = 0.995 ∙ 0.995 ∙ 0.995 ≈0.985

A card is selected at random from a standard deck without replacement A card is selected at random from a standard deck without replacement. Find the probability of selecting a diamond and a 7. What is our clue? and Which rule will we use? Multiplication rule Are the events independent or dependent? dependent 𝑃 𝑑𝑖𝑎𝑚𝑜𝑛𝑑 𝑎𝑛𝑑 7 =𝑃 𝑑𝑖𝑎𝑚𝑜𝑛𝑑 ∙𝑃 7|𝑑𝑖𝑎𝑚𝑜𝑛𝑑 = 13 52 ∙ 4 51 = 1 51 ≈0.020

A card is selected at random from a standard deck A card is selected at random from a standard deck. Find the probability of selecting a red suit or a queen. What is our clue? or Which rule will we use? Addition rule Are the events mutually exclusive? No 𝑃 𝑟𝑒𝑑 𝑜𝑟 𝑞𝑢𝑒𝑒𝑛 =𝑃 𝑟𝑒𝑑 +𝑃 𝑞𝑢𝑒𝑒𝑛 −𝑃 𝑟𝑒𝑑 𝑎𝑛𝑑 𝑞𝑢𝑒𝑒𝑛 = 26 52 + 4 52 − 2 52 ≈0.538

A card is selected at random from a standard deck A card is selected at random from a standard deck. Find the probability of selecting a 3 or a face card. What is our clue? or Which rule will we use? Addition rule Are the events mutually exclusive? yes 𝑃 3 𝑜𝑟 𝑓𝑎𝑐𝑒 𝑐𝑎𝑟𝑑 =𝑃 3 +𝑃 𝑓𝑎𝑐𝑒 𝑐𝑎𝑟𝑑 = 4 52 + 12 52 ≈0.308

Are the events independent or dependent? independent You flip a coin and roll a die. Find the probability of landing heads and rolling a number less than five. What is our clue? and Which rule will we use? Multiplication rule Are the events independent or dependent? independent 𝑃 ℎ𝑒𝑎𝑑𝑠 𝑎𝑛𝑑 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 5 =𝑃 ℎ𝑒𝑎𝑑𝑠 ∙𝑃 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 5 = 1 2 ∙ 4 6 = 4 12 ≈0.333

You roll a die. Find the probability of rolling a three or an even number. What is our clue? or Which rule will we use? Addition rule Are the events mutually exclusive? yes 𝑃 3 𝑜𝑟 𝑒𝑣𝑒𝑛 =𝑃 3 +𝑃 𝑒𝑣𝑒𝑛 = 1 6 + 3 6 ≈0.667