Exam 7: Probability

Use the following information for questions: A standard 52-card deck is shuffled and 2 cards are picked from the top of the deck. -The probability that the first card is a face card (Jack, Queen, King) and the second card is not a face card is

Michael wants to take French or Spanish, or both. But classes are closed, and he must apply and get accepted to be allowed to enroll in a language class. He has a 50% chance of being admitted to French, a 50% chance of being admitted to Spanish, and a 20% chance of being admitted to both French and Spanish. If he applies to both French and Spanish, the probability that he will be enrolled in either French or Spanish (or possibly both) is

Use the following information for questions: A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. -Suppose one study is to be randomly selected from all studies conducted over the past 3 years by this large research firm. What is the probability that this study used randomization?

Use the following information for questions: For each situation, decide if the probability described is a subjective (personal) probability or a relative frequency probability. -A recent college graduate claims he only has a 30% chance of finding a job in the next two months. The chance of 30% is a

Use the following information for questions: Students who live in the dorms at a college get free T.V. service in their rooms, but only receive 6 stations. On a certain evening, a student wants to watch T.V. and the six stations are broadcasting separate shows on baseball, football, basketball, local news, national news, and international news. The student is too tired to check which channels the shows are playing on, so the student picks a channel at random. -The two events A = {the student watches an athletic event} and N = {the student watches a news broadcast} are

Use the following information for questions: A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. -Define the events E = {the study was an experiment}, U = {the study used randomization} and R = {the study was a retrospective observational study}. Which of the following sets of events are disjoint?

A standard deck of cards has 52 cards. The cards have one of 4 suites: 13 cards are hearts, 13 cards are diamonds, 13 cards are clubs, and 13 cards are spades. We will draw cards from a shuffled deck of cards with replacement (after we draw each card, we will record the suite and put it back in the deck). We will keep going until we draw hearts. We wish to calculate the probability of having to draw 3 or fewer cards. Explain how you would choose random digits to simulate this scenario.

Use the following information for questions: The following table provides information regarding health status and smoking status of residents of a small community (health status for individuals was measured by the number of visits to the hospital during the year). -Are the events N = {the resident does not smoke} and Z = {the resident made zero visits to the hospital} mutually exclusive?

Use the following information for questions: In a survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of financial assistance. The correspondents were classified as to whether they currently had a child in college or not (college status), and whether they thought the loan obligation for most college students was too high, about right, or too little (loan obligation opinion). The table below summarizes some of the survey results. Use these results to answer the following questions. -What is the probability that a randomly selected adult with a child in college will think loan obligations are too high?

Elizabeth has just put 4 new spark plugs in her car. For each spark plug, the probability that it will fail in the next 50,000 miles is 1/100 (which is 0.01), and is independent from one spark plug to the next. What is the probability that none of the spark plugs will fail in the next 50,000 miles?

A birth is selected at random. Define events B = {the baby is a boy} and F = {the mother had the flu during her pregnancy}. The events B and F are

Use the following information for questions: In the Banana Republic there are two producers of PCs, referred to as Pac and Bell. Assume that there are no PC imports. The market shares for these two producers are 70% for Pac and 30% for Bell. One executive at Bell proposes a longer warranty period (similar to one given by auto makers) to be offered at a slight extra cost as a plan to increase market share. A market research company appointed by Bell conducts a census of PC owners on their opinion of this warranty proposal. Among owners of a PC made by Pac, 50% like the proposal, 30% are indifferent to it, while the remaining owners oppose it. Among owners of a PC made by Bell, 70% like the proposal, 20% are indifferent to it, and the remaining owners oppose it. -Suppose the selected PC owner is opposed to the new proposal. What is the conditional probability that the person is an owner of a PC made by Bell?

Use the following information for questions: For each of the following statements, determine if they are true or false. -If events D and E are known to be mutually exclusive, then P(D|E) = 0.

Use the following information for questions: A football player is randomly selected from all NCAA Division I college teams. Define the events D = {the football player plays defense} and T = {the football player is over 6 feet tall}. -How do we interpret the probability P(D|T)?

Use the following information for questions: A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. -Define the events E = {the study was an experiment} and U = {the study used randomization}. Are the events E and U independent?

A new drug is successful 80% of the time. A student would like to simulate the probability that if 5 people are given the drug it will be successful on exactly 3 of them. She will randomly choose digits with equal probability from 0, 1, 2, ..., 9 to represent each individual. How should she assign outcomes?

Use the following information for questions: It seems that every year we hear about a train derailment. Discussions about the safety of train travel are initiated each time. Suppose there have been nine fatal train derailments over the past 10 years. However, each year, 5 million train trips depart (this does not include subway travel). -What is the relative frequency of fatal train derailments?

Tree diagrams are most useful for finding probabilities when

When 2 cards are drawn at random from a standard 52-card deck, there is a 0.8507 chance of drawing 0 Aces, and a 0.1448 chance of drawing 1 Ace. What is the chance of drawing 2 Aces?

Use the following information for questions: A student is randomly selected from a large college. Define the events C = {the student owns a cell phone} and I = {the student owns an iPod}. -Which of the following is the correct notation for the percentage of students who own a cell phone but not an iPod?