Exam 3: Probability

Five people have collaborated on a new television show. Because they all have big egos, they each want their names listed first in the credits for the new show. How many different ways can the Names be ordered if they are randomly listed?

The probability of an event can be calculated by finding the sum of the probabilities of the individual sample points in the event and dividing by the number of sample points in the event.

The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a companyʹs success is customer service. A study was conducted to determine the customer Satisfaction levels for one overnight shipping business. In addition to the customerʹs satisfaction Level, the customers were asked how often they used overnight shipping. The results are shown Below in the following table: A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that the customer expressed low satisfaction with the company?

A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below. Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years?

A hospital reports that two patients have been admitted who have contracted Crohnʹs disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of The disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 Dies, etc.). Simple Events Probabilities SS 0.55 SD 0.11 DS 0.13 DD 0.21 Find the probability that at least one of the patients does not survive.

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} Identify the sample points in the event A ∪ B.

Suppose that an experiment has five sample points, $E _ { 1 } , E _ { 2 } , E _ { 3 } , E _ { 4 } , E _ { 5 }$ , and that $P \left( E _ { 1 } \right) = .4$ , $P \left( E _ { 2 } \right) = .1 , P \left( E _ { 3 } \right) = .1 , P \left( E _ { 4 } \right) = .2$ , and $P \left( E _ { 5 } \right) = .2$ . If the events $A$ and $B$ are defined as $A = \left\{ E _ { 1 } , E _ { 2 } , E _ { 5 } \right\}$ and $B = \left\{ E _ { 2 } , E _ { 3 } , E _ { 5 } \right\}$ find $P ( A \cup B )$ .

A consumer testing service is commissioned to rank the top 4 brands of dishwasher detergent. Ten brands are to be included in the study. In how many different ways can the consumer testing service arrive at the ranking?

The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let $A$ be the event that the number rolled is less than 4 , and let $B$ be the event that the number rolled is odd. Find $P ( A \cup B )$ .

Suppose there is a 40% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in three independent risky stocks. What is the probability that all three stocks end up in total losses?

Suppose that 80% of the employees of a company received cash or company stock as a bonus at the end of the year. If 60% of the employees received a cash bonus and 30% received stock, what is the probability that a randomly chosen employee received both cash and stock as a bonus?

National Brand B fabric softener is among 10 brands being rated by a consumer group. If the group ranks the brands at random, what is the probability that National Brand B fabric softener will be ranked in the top three?

A number between 1 and 10, inclusive, is randomly chosen. Events A, B, C, and D are defined as follows. A: {The number is even} B: {The number is less than 7} C: {The number is odd} D: {The number is greater than 5} Identify one pair of mutually exclusive events.

An event and its complement are mutually exclusive.

At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student receives some form of government-sponsored financial aid.

Suppose that for a certain experiment $P ( A ) = 0.6$ and $P ( B ) = 0.3$ . If $A$ and $B$ are independent events, find $P ( A \cap B )$ .

Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male or received a merit raise?

Find the numerical value. -You toss one coin and one die. What is the probability of getting heads and a number greater than 3?

The table shows the number of each Ford car sold in the United States in June 2006. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Events A and B are defined as follows. A: {Convertible, SUV, Van} B: {Fewer than 10,000 of the type of car were sold in June 2006} $\text { Find } P(A \mid B) \text { and } P(B \mid A)$ .