Exam 8: Probability

Use a tree diagram to find the indicated probability. -In the town of Cheraw,a certain type of laptop computer is sold at just two stores.Store A has 38% of the sales, 4% of which are of defective items,and store B has 62% of the sales,2% of which are of defective items.A Person receives one of these laptop computers as a gift.What is the probability it is defective?

A fair die and a fair coin are tossed in succession.Find the sample space composed of equally likely events.

Find the probability. -A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that among 7 randomly selected graduates,at least one finds a job in his or her chosen field within a year of graduating.

Provide an appropriate response. -The number of loaves of whole wheat bread left on the shelf of a local quick stop at closing (denoted by the random variable X)varies from day to day.Past records show that the probability distribution of X is as shown in the following table.Find the probability that there will be at least three loaves left over at the end of any given day.

List the outcomes of the sample space. -A box contains 10 blue cards numbered 1 through 10.List the sample space of picking one card from the box.

Estimate the indicated probability. -College students were given three choices of pizza toppings and asked to choose one favorite.The following table shows the results. A randomly selected student prefers a cheese topping.

Use Bayes' rule to find the indicated probability. -An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R)= 0.53.The clay probability is P(C)= 0.21.The sand probability is P(S)= 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is clay,P(clay | positive)?

Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. -Two marbles are drawn from a bag in which there are 4 red marble and 2 blue marble.The number of blue marbles is counted.

Use Bayes' rule to find the indicated probability. -Two stores sell a certain MP3 players.Store A has 34% of the sales,5% of which are of defective items,and store B has 66% of the sales,1% of which are of defective items.The difference in defective rates is due to different levels of pre-sale checking of the product.A person receives a defective item of this product as a gift.What is the probability it came from store B?

Find the probability. -Samantha is taking courses in math and English.The probability of passing math is estimated at 0.4 and English at 0.6.She also estimates that the probability of passing at least one of them is 0.8.What is her probability of passing both courses?

Determine independence. Answer Yes or No. -According to a survey,8% of students at a college are left handed,53% are female,and 4.24% are both female and left handed.Is being left handed independent of gender?

In a survey of the number of DVDs in a house, the table shows the probabilities. -Find the probability of a house having fewer than 2 DVDs.

Use Bayes' rule to find the indicated probability. -An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R)= 0.53.The clay probability is P(C)= 0.21.The sand probability is P(S)= 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is rock,P(rock | positive)?

Use a tree diagram to find the indicated probability. -3.9% of a secluded island tribe are infected with a certain disease.There is a test for the disease,however the test is not completely accurate.92% of those who have the disease will test positive.However 4.4% 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.

Find the expected value. -Mr.Cameron is sponsoring an summer concert.He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain.The weather bureau predicts the chance of rain is 0.34 for the day of the concert.An insurance company is willing to insure the concert for $150,000 against rain for a premium of $30,000.If he buys this policy,what are his expected earnings from the concert?

Determine independence. Answer Yes or No. -A group of 25 people contains 10 brunettes,8 blondes,and 7 redheads.Of the 20 girls in the group,8 are brunettes,6 are blondes,and 6 are redheads.A person is selected at random.Are the events of being a girl and having brown hair independent?

If 82% of scheduled flights actually take place and cancellations are independent events,what is the probability that 3 separate flights will all take place?

Use Bayes' rule to find the indicated probability. -In Cumberland County,55% of registered voters are Democrats,30% are Republicans and 15% are independent. During a recent election,35% of the Democrats voted,65% of the Republicans voted,and 75% of the Independent voted.What is the probability that someone who voted is a Democrat?

Find the odds. -In a certain town,20% of people commute to work by bus.If a person is selected randomly from the town,what are the odds against selecting someone who commutes by bus?

Find the expected value. -A new light bulb has been found to have a 0.02 probability of being defective.A shop owner receives 500 bulbs of this kind.How many of these bulbs are expected to be defective?