Exam 13: Probability Rules

The table shows the careers of a group of retired people and their ages at retirement. Age at Retirement Career 50-55 56-60 61-65 Over 65 Total Attorney 9 49 96 40 194 College Professor 8 50 91 42 191 Secretary 21 45 63 49 178 Store Clerk 18 44 70 50 182 Total 56 188 320 181 745 What is the probability that a person who retired between the ages of 56 and 60 was a college professor?

A group of volunteers for a clinical trial consists of 86 women and 79 men.20 of the women and 21 of the men have high blood pressure.If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

In a small town,a certain type of laptop computer is sold at just two stores.Store A has 31% of the sales,3% of which are of defective items,and store B has 69% of the sales,5% of which are of defective items.A person receives one of these laptop computers as a gift.What is the probability it is defective?

If a single fair die is rolled,find the probability of a 5 given that the number rolled is odd.

1.8% of a population is infected with a certain disease.There is a test for the disease; however,the test is not completely accurate.94.2% of those who have the disease will test positive.However 4.8% of those who do not have the disease will also test positive (false positives).What is the probability that a person who tests positive actually has the disease?

In one town in British Columbia,only 20% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,1.4% of employees will call in sick.What percent of calls (where an employee calls in sick)occur on sunny days?

In one town in British Columbia,only 27% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,1.0% of employees will call in sick.Is calling in sick independent of sunshine? Explain.

You roll a fair die six times.What is the probability that you roll at least one 5?

A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers.It buys 23% of the connectors from supplier A,31% from supplier B,and 46% from supplier C.It finds that 1% of the connectors from supplier A are defective,2% of the connectors from supplier B are defective,and 3% of the connectors from supplier C are defective.If a customer buys one of these components and finds that the connector is defective,what is the probability that it came from supplier B?

The date is March 8,and there are 104 people in a room.What is the probability that at least one of them has a birthday today?

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As),the Ace of Hearts (Ah),the King of Spades (Ks)and the 9 of Hearts (9h).Aces count as 1 or 11.Kings count as 10.You are interested in the total count of the two cards,with a maximum count of 21 (that is,AsAh = 12).Given that the total count is at least 19,what is the probability that the hand contains the King of Spades?

1.9% of a population is infected with a certain disease.There is a test for the disease; however,the test is not completely accurate.91% of those who have the disease will test positive.However 3.6% of those who do not have the disease will also test positive (false positives).What is the probability that any given person will test positive? Round your answer to three decimal places if necessary.

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a face card given that it is a king.

A company is conducting a sweepstakes,and ships two boxes of game pieces to a particular store.4% of the contents of box A are winners,while 6% of the contents of box B are winners.Box A contains 36% of the total tickets.If the contents of both boxes are mixed in a drawer and a ticket is chosen at random,what is the probability it is a winner?

Some employers use lie detector tests to screen job applicants.Lie detector tests are not completely reliable.Suppose that a polygraph can detect 64% of lies,but incorrectly identifies 16% of true statements as lies.A company gives its job applicants a polygraph test,asking "Did you tell the truth on your job application?".All the applicants answer "Yes",but the test identifies some of those answers as lies,thereby causing the person to fail the test.Suppose that 90% of the job applicants tell the truth during the polygraph test.What is the probability that a person who fails the test was actually telling the truth?

Among the contestants in a competition are 50 women and 29 men.If 5 winners are randomly selected,what is the probability that they are all men? Round your answer to five decimal places.

The table shows the popular votes cast in the U.S.A in the 1984 presidential election classified by region and political party.Data are in thousands,rounded to the nearest thousand. Political Party Region Demo. Repub. Other Total Northeast 9046 11,336 101 20,483 Midwest 10,511 14,761 169 25,441 South 10,998 17,699 136 28,833 West 7022 10,659 214 17,895 Total 37,577 54,455 620 92,652 Find the probability that a voter who lives in the Northeast voted Democrat.

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As),the Ace of Hearts (Ah),the King of Spades (Ks)and the 9 of Hearts (9h).Given that the hand contains at least one Ace,what is the probability that it contains both Aces?

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As),the Ace of Hearts (Ah),the King of Spades (Ks)and the 9 of Hearts (9h).Aces count as 1 or 11.Kings count as 10.You are interested in the total count of the two cards,with a maximum count of 21 (that is,AsAh = 12).If the total of the two cards dealt out is higher than the total of the two remaining cards you win the game.Is winning independent or dependent of the event of having exactly one Ace?

In driving a car,the events of driving over the speed limit and getting a speeding ticket