Exam 2: Probability Concepts and Applications

Saying that a set of events is collectively exhaustive implies that one of the events must occur.

Using the table for finding the areas under normal curves, find the area under a normal curve with a mean of 200 and a standard deviation of 10 between the values of: (a) 200 to 205. (b) 195 to 205. (c) 200 to 215. (d) 195 to 215. (e) 186.5 to 217.

If two events (A,B) are independent, what is their joint probability?

Assume that you have an urn containing 10 balls of the following description: 4 are white (W) and lettered (L) 2 are white (W) and numbered (N) 3 are yellow (Y) and lettered (L) 1 is yellow (Y) and numbered (N) If you draw a lettered ball (L), the probability that this ball is white (W) is 0.571.

A market research study is being conducted to determine if a product modification will be well received by the public. A total of 1,000 consumers are questioned regarding this product. The table below provides information regarding this sample. (a) What is the probability that a randomly selected male would find this change unfavorable (negative)? (b) What is the probability that a randomly selected person would be a female who had a positive reaction? (c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances.

The number of bad checks written at a local store is an example of a discrete random variable.

A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below. On average, she should expect 0.8 interruptions per hour.

The variance of a binomial distribution is expressed as np/(1-p), where n equals the number of trials and p equals the probability of success of any individual trial.

A new television program was viewed by 200 people (120 females and 80 males). Of the females, 60 liked the program and 60 did not. Of the males, 60 of the 80 liked the program. (a) What is the probability that a randomly selected individual liked the program? (b) If a male in this group is selected, what is the probability that he liked the program? (c) What is the probability that a randomly selected individual is a female and liked the program?

An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the probability of: (a) drawing three yellow chips. (b) drawing a blue chip on the first draw and a yellow chip on the second draw. (c) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw. (d) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw. (e) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw.

If a bucket has three black balls and seven green balls, and we draw balls without replacement, the probability of drawing a green ball is independent of the number of balls previously drawn.

If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is greater than $110?

A company is considering producing two new electronic games designed for the popular Gameboy toy. Based on market data, management believes that there is a 60 percent chance that a "cops and robbers" game will be successful and a 40 percent chance that "let's play house" game will be successful. As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other. If two products are introduced to the market, what is the probability that both are failures?

The expected value of a probability distribution is

A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful?

The length of time that it takes the tollbooth attendant to service each driver can typically be described by the

A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that the second item will be defective?

Explain why event probabilities range from 0 to 1.