Exam 4: Probability

Describe an event whose probability of occurring is 1 and explain what that probability means. Describe an event whose probability of occurring is 0 and explain what that probability means.

In a homicide case 8 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 8 witnesses would pick the same person.

How many ways can an IRS auditor select 6 of 13 tax returns for an audit?

Use Bayes' theorem to find the indicated probability. -Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 63% of lies are identified as lies and that 16% of true statements are also identified as lies. A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job application?". 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?

What important question must you answer before computing an "or" probability? How does the answer influence your computation?

A 6-sided die is rolled. Find P(3 or 5).

A class has 11 students who are to be assigned seating by lot. What is the probability that the students will be arranged in order from shortest to tallest? (Assume that no two students are the same height.)

Find the indicated probability. -On a multiple choice test, each question has 3 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

From the information provided, create the sample space of possible outcomes. -Flip a coin twice.

Express the indicated degree of likelihood as a probability value. -"It will definitely turn dark tonight."

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. -The following table contains data from a study of two airlines which fly to Small Town, USA. Number of flights Number of flights which were on time which were late Podunk Airlines 33 6 Upstate Airlines 43 5 If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time.

From the information provided, create the sample space of possible outcomes. -Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.

Determine whether the events are disjoint. -Meet a man with an umbrella. Meet a man with a raincoat.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Assume that a study of 300 randomly selected school bus routes showed that 281 arrived on time. Is it "unusual" for a school bus to arrive late?

Use Bayes' theorem to find the indicated probability. -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 0.06. If it doesn't rain, The probability that he will miss his flight is 0.02. The probability that it will rain on Monday is 0.29. Suppose that Shameel misses his flight. What is the probability that it was raining?

Which of the following cannot be a probability?

Estimate the probability of the event. -A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: $0 =$ FOR, 1 = AGAINST . If the referendum were held today, estimate the probability that it would pass. $0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0$

The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 404 34 32 470 Women 375 39 50 464 Total 779 73 82 934 If two different people are randomly selected from the 934 subjects, find the probability that they are both women. Round to four decimal places.

How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).