Exam 14: Probability Rules

The sales bin in a clothing store contains an assortment of t-shirts in different sizes.There are 4 small,7 medium,and 9 large shirts.Alan is looking for a large shirt.He starts grabbing shirts one at a time and checking the size.After he checks each shirt,he leaves it outside the bin.What is the probability that the first large shirt he finds is the third one he checks?

63% of students at one college drink coffee,and 16% of people who drink coffee suffer from insomnia.What is the probability that a randomly selected student drinks coffee and suffers from insomnia?

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?

In a business class,15% of the students have never taken a statistics class,40% have taken only one semester of statistics,and the rest have taken two or more semesters of statistics.The professor randomly assigns students to groups of three to work on a project for the course.What is the probability that neither of your two group mates has studied statistics?

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one red card.

Shameel has a flight to catch on Monday morning.His father will give him a ride to the airport.If it rains,the traffic will be bad and the probability that he will miss his flight is 0.04.If it doesn't rain,the probability that he will miss his flight is 0.01.The probability that it will rain on Monday is 0.28.Are rain and Shameel missing his flight independent events? Explain.

You roll a fair die six times.What is the probability that you roll all 5's?

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.

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a three given that it is not a face card.

Opinion-polling organizations sometimes contact their respondents by sampling random telephone numbers.Assume that interviewers can now reach about 78% of Canadian households,while the percentage of those contacted who agree to cooperate with the survey is 36%.Each household,of course,is independent of the others.What is the probability of obtaining an interview with the next household on the sample list?

A high school offers these statistics: 59% of incoming students come from single-parent homes. 41% of incoming students come from two-parent homes. 21% of incoming students from single-parent homes eventually go on to get a college education. 44% of incoming students from two-parent homes eventually go on to get a college education. What percent of students who get a college education come from single-parent families?

A group of volunteers for a clinical trial consists of 79 women and 77 men.20 of the women and 18 of the men have high blood pressure.If one of the volunteers is selected at random find the probability that the person is a man given that they have high blood pressure.

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

1.8% of a population are 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 rolling a fair die once,the events of getting a 3 and getting a 6

A box contains 16 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that she has to pick 5 batteries in order to find one that works.

A box contains batteries of which 48 are defective and 24 are good.You start picking batteries one at a time and testing them.What is the probability that the first four batteries you pick are all defective?

A group of volunteers for a clinical trial consists of 88 women and 90 men.20 of the women and 19 of the men have high blood pressure.Are high blood pressure and gender independent? Explain.

You are dealt a hand of three cards,one at a time.Find the probability that you get no clubs.

There is a huge pile of buttons in which 28% are black,14% are blue,20% are orange,22% are white,and the rest are clear.You close your eyes,choose a button at random,write down what colour it is,and then put it back in the pile.What is the probability that the third button you choose is the first one that's clear?