The complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by _______.
The difference between classical and empirical probability is that classical probability assumes that certain outcomes are equally likely while empirical probability relies on actual observation to determine the likelihood of outcomes.
The director of the Readlot College Health Center wishes to open an eye clinic. To justify the expense of such a clinic, the director reports the probability that a student selected at random from the college roster needs corrective lenses. He took a random sample of 500 students to compute this probability and found that 375 of them need corrective lenses. What is the probability that a Readlot College student selected at random needs corrective lenses?
The Right to Health Lobby wants to make a claim about the number of erroneous reports issued by a medical lab in one low-cost health center. Suppose they find in a random sample of 100 reports, 40 erroneous lab reports. What’s the probability that a report issued by this health center is erroneous?
An automobile dealer has 10 Fords, 7 Buicks, and 5 Plymouths on her used car lot. If a person purchases a used car, find the probability that it is a Ford or a Buick?
An automobile dealership has found that 37 percent of its new car sales have been dealer financed, 45 percent have been financed by another institution, and 18 percent have been cash sales. Find the probability that the next purchase of a new car at this dealership will be either a cash sale or dealer financed.
The probability that a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55.
What is the probability that a given student owns a car or a computer?
The probability that a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55.
What is the probability that a given student owns neither a car nor a computer?
At a used-book sale, 100 books are adult books and 160 are children’s books. Seventy of the adult books are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability that it is
Fiction
not a children’s nonfiction
an adult book or a children’s nonfiction
45.
4-4 The Multiplication Rules and Conditional Probability
Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring.
One card is selected from a deck of 52 cards and replaced and then another card is selected. Find the probability of selecting a queen and then selecting a heart.
The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If four people are selected at random, find the probability that they all used a seat belt the last time they got into a car.
When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent events.
The conditional probability of an event B in relationship to an event A is the probability that event B occurs after event A has already occurred. The notation for conditional probability is P(B|A).
A flashlight has six batteries, two of which are defective. If two are selected at random without replacement, find the probability that both are defective.
In a class containing twelve men and two women, 2 students are selected at random to given an impromptu speech. Find the probability that both are men.
An automobile manufacturer has three factories, A, B, and C. They produce 50%, 30%, and 20%, respectively of a specific model of car. Thirty percent of the cars produced in factory A are white, 40% of those produced in factory B are white, and 25% of those produced in factory C are white. If an automobile produced by the company is selected at random, find the probability that it is white.
The probability that the second event B occurs given that the first event A has already occurred can be found by dividing the probability that both events occurred by the probability that the first event occurred.
At a small college, the probability that a student takes physics and sociology is 0.092. The probability that a student takes sociology is 0.73. Find the probability that the student is taking physics, given that he or she is taking sociology.
A circuit to run a model railroad has eight switches. Two are defective. If a person selects two switches at random and tests them, find the probability that the second one is defective, given that the first one is defective.
In a pizza restaurant, 95% of the customers order pizza. If 65%of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad.
The probability that it snows and the bus arrives late is 0.023. John hears the weather forecast, and there is a 40% chance of snow tomorrow. Find the probability that the bus will be late, given that it snows.
Try at Home for Next Time - Thirteen percent of the employees of a large company are female technicians. Forty percent of its workers are technicians. If a technician has been assigned to a particular job, what is the probability that the person is female?
Traffic entering an intersection can continue straight ahead or turn right. Eighty percent of the traffic flow is straight ahead. If a car continues straight, the probability of a collision is 0.0004; if a car turns right, the probability of a collision is 0.0036. Find the probability that a car entering the intersection will have a collision.
In situations where it is critical that a system function properly, additional backup systems are usually provided. Suppose a switch is used to activate a component in a satellite. If the switch fails, then a second switch takes over and activates the component. If each switch has a probability of 0.002 of failing, what is the probability that the component will be activated?
A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, find the probability that he or she will contract the disease.
A game is played by drawing four cards from an ordinary deck and replacing each card after it is drawn. Find the probability of winning if at least one ace is drawn.
It has been found that 40% of all people over the age of 85 suffer from Alzheimer’s disease. If three people over 85 are selected at random, find the probability that at least one person does not suffer from Alzheimer’s disease.
In a lab there are eight technicians. Three are male and five are female. If three technicians are selected, find the probability that at least one is female.
On a surprise quiz consisting of five true-false questions, an unprepared student guesses each answer. Find the probability that he gets at least one correct.
A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medications, at least one person’s infection will not improve.
In a sequence of n events in which the first one has k possibilities and the second has k 2 possibilities and the third has k 3 possiblities and so fourth, the total number of possibilities of the sequence would be k 1 * k 2 * k 3 . . . .
There are eight different statistics books, 6 different geometry books and 3 different trigonometry books. A student must select one book of each type. How many different ways can this be done?
A college bookstore offers a personal computer system consisting of a computer, a monitor, and a printer. A student has a choice of two computers, three monitors, and two printers, all of which are compatible. In how many ways can a computer system be bundled?
You are hosting a dinner party for eight people. In preparing the seating arrangement, you would like to know the number of different ways in which the guest can be arranged.
The board of directors of a local college has 12 members. Three officers—president, vice-president and treasurer—must be elected from the members. How many different possible slates of officers are there?
A sales representative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. There are air connections between each of the cities. In how many orders can he visit the cities?
A pizza shop offers a combination pizza consisting of a choice of any three of the four ingredients: pepperoni (P), mushrooms (M), sausage (S), and anchovies (A). Determine the number of possible combination pizzas.
There are three nursing positions to be filled at Lilly Hospital. Position one is the day nursing supervisor; position two is the night nursing supervisor; and position three is the nursing coordinator position. There are 15 candidates qualified for all three of the positions. In how many ways can the positions be filled by the applicants?
A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.)
A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.)
A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.)
A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.)
An instructor gives her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz?
What’s the probability that the student gets a score of 100?
An instructor give her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz?
What’s the probability that the student gets a score of 80?
An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting:
An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting:
An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting:
An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting:
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