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Exam 4: Probability

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Question 51

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If the probability that someone likes the color blue is 44% and the probability that among those individuals, the probability that they wake up early is 52%, then the probability that individuals who like the color blue and wake up early is about 23%.

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Question 52

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If the occurrence of one event does not affect the occurrence of another event, then the two events are mutually exclusive.

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Question 53

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A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A, B, and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected, what is the probability that the person prefers design A?

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A, B, and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected, what is the probability that the person prefers design A and is under 25?

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

The list of all elementary events for an experiment is called the sample space.

Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.A student is randomly selected, what is the probability that the student is enrolled in either accounting or statistics or both?

Suppose that 3% of all TVs made by a company in 2018 are defective.If 2 of these TVs are randomly selected what is the probability that both are defective?

The general law of addition is P(X $\cap$ Y)= P(X)+ P(Y)- P(X $\cup$ Y).

Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.A student is randomly selected, and it is found that the student is enrolled in accounting.What is the probability that this student is also enrolled in statistics?

P(B $\mid$ A)denotes a conditional probability.

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are independent.

Probability is used to develop knowledge of the fundamental mathematical tools for quantitatively assessing risk.

In a set of 10 aluminum castings, two castings are defective (D) , and the remaining eight are good (G) .A quality control inspector randomly selects three of the ten castings with replacement and classifies each as defective (D) or good (G) .How large is the sample space?

The list of all elementary events for an experiment is called ___.

Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the relative frequency of occurrence method.

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%.In this case, the two events are independent.

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D) , 90% of all personal loans are not in default (D΄) , 20% of those in default are homeowners (H | D) , and 70% of those not in default are homeowners (H | D΄) .If a personal loan is selected at random P (H $\cap$ D') = ___.