0.15 More probability: homework  (Page 5/5)

Suppose a test is given to determine if a person is infected with HIV. If a person is infected with HIV, the test will detect it in 90% of the cases; and if the person is not infected with HIV, the test will show a positive result 3% of the time. If we assume that 2% of the population is actually infected with HIV, what is the probability that a person obtaining a positive result is actually infected with HIV?

A movie and music rental store's inventory consists of 70% movie videos and 30% music videos. Twenty percent of the movie videos and 10% of the music videos are old and need replacement. If a video chosen at random is found to be old, what is the probability that it is a movie video?

Two machines make all the products in a factory, with the first machine making 30% of the products and the second 70%. The first machine makes defective products 3% of the time and the second machine 5% of the time.

1. Overall what percent of the products made are defective?

2. If a defective product is found, what is the probability that it was made on the second machine?

3. If it was made on the second machine, what is the probability that it is defective?

An instructor in a finite math course estimates that a student who does his homework has a 90% of chance of passing the course, while a student who does not do the homework has only a 20% chance of passing the course. It has been determined that 60% of the students in a large class do their homework.

1. What percent of all the students will pass?
2. If a student passes, what is the probability that he did the homework?

Cars are being produced by three factories. Factory I produces 10% of the cars and it is known to produce 2% defective cars, Factory II produces 20% of the cars and it produces 3% defective cars, and Factory III produces 70% of the cars and 4% of those are defective. A car is chosen at random. Find the following probabilities:

1. $P\left(\text{The car is defective}\right)$
2. $P\left(\text{It came from Factory III}\mid \text{the car is defective}\right)$

A multiple-choice test has five choices to a question and only one of them is correct. If a student does his homework, he has a 90% of chance of getting the correct answer. Suppose there is a 70% chance that the student will do his homework, what will his test score be on this test?

A game involves rolling a pair of dice. One receives the sum of the face value of both dice in dollars. How much should one be willing to pay to roll the dice to make the game fair?

A roulette wheel consists of numbers 1 through 36, 0, and 00. If the wheel comes up an odd number you win a dollar, otherwise you lose a dollar. If you play the game ten times, what is your expectation?

A student takes a 100-question multiple-choice exam in which there are four choices to each question. If the student is just guessing the answers, what score can he expect?

Mr. Shaw invests 50% of his money in stocks, 30% in mutual funds, and the remaining 20% in bonds. If the annual yield from stocks is 10%, from mutual funds 12%, and from bonds 7%, what percent return can Mr. Shaw expect on his money?

An insurance company is planning to insure a group of surgeons against medical malpractice. Its research shows that two surgeons in every fifteen are involved in a medical malpractice suit each year where the average award to the victim is $450,000. How much minimum annual premium should the insurance company charge each doctor?

In an evening finite math class of 30 students, it was discovered that 5 students were of age 20, 8 students were about 25 years old, 10 students were close to 30, 4 students were 35, 2 students were 40 and one student 55. What is the average age of a student in this class?

Jar I contains 4 marbles of which one is red, and Jar II contains 6 marbles of which 3 are red. Katy selects a jar and then chooses a marble. If the marble is red, she gets paid 3 dollars, otherwise she loses a dollar. If she plays this game ten times, what is her expected payoff?

Jar I contains 1 red and 3 white, and Jar II contains 2 red and 3 white marbles. A marble is drawn from Jar I and put in Jar II. Now if one marble is drawn from Jar II, what is the probability that it is a red marble?

Let us suppose there are three traffic lights between your house and the school. The chance of finding the first light green is 60%, the second 50%, and the third 30%. What is the probability that on your way to school, you will find at least two lights green?

Sonya has just earned her law degree and is planning to take the bar exam. If her chance of passing the bar exam is 65% on each try, what is the probability that she will pass the exam in at least three tries?

Every time Ken Griffey is at bat, his probability of getting a hit is .3, his probability of walking is .1, and his probability of being struck out is .4. If he is at bat three times, what is the probability that he will get two hits and one walk?

Jar I contains 4 marbles of which none are red, and Jar II contains 6 marbles of which 4 are red. Juan first chooses a jar and then from it he chooses a marble. After the chosen marble is replaced, Mary repeats the same experiment. What is the probability that at least one of them chooses a red marble?

Andre and Pete are two tennis players with equal ability. Andre makes the following offer to Pete: We will not play more than four games, and anytime I win more games than you, I am declared a winner and we stop. Draw a tree diagram and determine Andre's probability of winning.