Exam 4: Probability

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?

Suppose that the probability that LIBOR (London inter-bank offered rate)will increase next trimester is 0.025.Assume also that the probability that your company will open a new branch overseas is 0.20.If the probability that at least one of the two events occur,i.e.,LIBOR increases and/or your company opens a new overseas branch,is 0.21,what is the probability that both events occur?

A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting the success. Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail). In the past,for all new products that ultimately were successful,80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures). Also,for all new products that were ultimately failures,70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes). What is the a priori probability that a new product would be a success?

Max Sandlin is exploring the characteristics of stock market investors. He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage. An investor is selected randomly,and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= _____________.

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year,P (Male)= ________

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

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 overweight given that this student exercises regularly?

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 table below provides summary information about students in a class. The sex of each individual and their age is given. If a student is randomly selected from this group,what is the probability that the student is a female who in under 20 years old?

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 (D | H)= ___________.

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in an finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. Find P(S).

If two events are mutually exclusive,then their joint probability is always zero.

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 classical method.

Max Sandlin is exploring the characteristics of stock market investors. He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage. An investor is selected randomly,and E is the event "net worth exceeds $1,000,000," and O is the event "uses an online brokerage." P(O|E)= _____________.

Suppose you toss a fair coin three times in a row and obtain tails,tails,and tails.What it the probability that the fourth toss will give heads?

Suppose that 3% of all TVs made by some Company in 2012 are defective.If 2 of these TVs are randomly selected what is the probability that both are defective?

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?

If X and Y are mutually exclusive events,then if X occurs _______.

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

Your company provides services to three different industries: automotive,construction,and financial services.These services can be either on a yearly or on a monthly contract.The cross-tabulation table below summarizes this information: Suppose you know that a given client is a construction company and you are interested in the likelihood that this client is on a yearly contract.This is an example of _______.