Exam 14: Probability Rules

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 both of your two group mates have studied at least one semester of statistics?

A box contains 14 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 at least one of the first four works.

University students were given three choices of pizza toppings and asked to choose one favorite.They were also asked what year of their program they were in.The following table shows the results. Among the students in their third year,what is the probability that a student responded "meat"?

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

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all diamonds.

A teacher designs a test so that 92% of students who study will pass and 7% of students who don't study will pass.94% of students study for a test.What is the probability that a randomly selected student passes?

In rolling a fair die twice,the events of getting a 1 on the first roll and a 5 on the second

A bag contains 5 red chips and 12 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are both red?

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?

A consumer organization estimates that 32% of the households in a particular community have one television set,38% have two sets,and 16% have three or more sets.If two households are chosen at random,what is the probability that at least one has one ore more television sets?