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Probability and combinatorics

### A license plate is designed so that the first two characters are letters and the last four characters are digits. How many different license plates can be formed assuming that letters and numbers can be used more than once

Probability and combinatorics

### Suppose that the probability density function of the amount of milk deposited in a milk container is: $$\displaystyle{f{{\left({X}\right)}}}={40.976}-{16}{x}^{{2}}-{30}{e}^{{-{x}}}$$ for $$\displaystyle{1.95}\le{x}\le{2.1}$$ Liters. a) Calculate the probability that the actual amount of milk deposited is less than 2 liters. b) Calculate the Expected Value in Liters of this distribution.

Probability and combinatorics

### A license plate is designed so that the first two characters are letters and the last four characters are digits​ (0 through​ 9). How many different license plates can be formed assuming that letters and numbers can be used more than​ once?

Probability and combinatorics

### How many five-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?

Probability and combinatorics

### where 30% of all admitted patients fail to pay their bills and the debts are eventually forgiven. suppose that the clinic treats 2000 different patients over a period of 1 year, and let x be the number of forgiven debts. a. what is the mean (expected) number of debts that have to be forgiven? b. find the variance and standard deviation of x. c. what can you say about the probability that x will exceed 700?

Probability and combinatorics

### Suppose that you buy a lottery ticket containing k distinct numbers from among $\left\{1,2,...,n\right\}, 1\leq k \leq n$. To determine the winning tickets, k balls are randomly drawn without replacement from a bin containing n balls numbered 1, 2, . . . , n. What is the probability that at least one of the numbers on your lottery ticket is among those drawn from the bin?

Probability and combinatorics

### Urn 1 contains 7 red balls and 1 black ball. Urn 2 contains 1 red ball and 2 black balls. Urn 3 contains 5 red balls and 2 black balls. If an urn is selected at random and ball is drawn, find the probability that it will be red.

Probability and combinatorics

### A ping test determines whether a client (computer, smartphone, or similar device) communicates with another device across a network. Assume that the probability of response to a test is 3/4. The test involves a large number of runs and it continues until the first response is recorded. Define the random variable X as the number of runs of the test required to terminate the experiment. Suppose that the condition of one run does not affect that of another. a. Determine the probability distribution of X. b. Let A be defined as the event that the experiment ends after an even number of repetitions. Evaluate P(A).

Probability and combinatorics

### Suppose 38 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will be between $30.00 and$31.00?

Probability and combinatorics

### There are 5 women and 3 men waiting on standby for a flight to New York. Suppose 3 of these 8 people are selected at random, and a random variable X is defined to be the number of women selected. Find Pr[X = 2].

Probability and combinatorics

### Kate and Helena were playing a card game with a 25 card deckk. Kate added 6 cards to the stack. Then she took 7 cards away. Helena took 5 cards. How many cards remained in the deck?

Probability and combinatorics

### A report revealed that the average number of months that an employee stays in a factory is 36 months. Assuming that the number of months of an employee tenure in the factory is normally distributed with a standard deviation of 6 months, find the probability that a certain employee will stay. a. More than 30 months b. Less than 24 months c. Between 24 to 48 months

Probability and combinatorics

### In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?

Probability and combinatorics

### A restaurant offers a \$12 dinner special that has 7 choices for an appetizer, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?

Probability and combinatorics

### A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true. If the questions can be positioned in any order, how many different answer keys are possible?

Probability and combinatorics

### In a criminal trial b jury, suppose the probability the defendant is convicted, given guilt, is 0,95, and the probability the defendant is acquitted , given innocence, is 0,95. Suppose that 83% of all defendants truly are guilty. Given that the defendant is convicted, find the probability he or she was actually innocent.

Probability and combinatorics

### Your manager will assign her 9 employees to three tasks, 2 to task A, 4 to task B, and 3 to task C. If she randomly assigns employees to tasks, what is the probability that you and your best friend will be the two assigned to task A?

Probability and combinatorics

### Suppose $$\displaystyle{E}{\left({X}\right)}={5}$$ and $$\displaystyle{E}{\left[{X}{\left({X}–{1}\right)}\right]}={27.5},$$ find $$\displaystyle\in{\left({x}^{{2}}\right)}$$ and the variance.

Probability and combinatorics