Finite Analysis PROF DOUBLE R

I.

Find the number using the following Venn diagram.

n(U)

Sorry, an error occurred while generating this image. Please return to your home page and open this assignment again. If you still have problems, click Help, and then Contact Us to report this error. We are sorry for the inconvenience.

2.

Find the number using the following Venn diagram.

15

3. Find the number using the following Venn diagram.

4.

5.

How many seven-symbol computer passwords can be formed using the letters A to J and the digits 3 to 5? Passwords

6.

7.

Determine the number of permutations.

8.

Find the number of combinations.

9.

A computer password is to consist of five alphanumeric characters with no repeats. (An alphanumeric character is a letter from A to Z or a digit from 0 to 9.)

How many such passwords are there?

Passwords

How many are there if the letter O and the digit 0 are excluded to avoid confusion? passwords

10.

A junior high girls' basketball team is to consist of 5 players. How many different teams can the manager select from a roster of 10 girls? teams

11.

If a committee of 3 is to be chosen at random from a class of 15 students, what is the probability of any particular committee being selected? (Enter your answer as a fraction.)

What if the committee is to consist of a president, a vice president, and a treasurer? (Enter your answer as a fraction.)

12.

A box contains 5 red and 6 green marbles. You reach in and remove 3 marbles all at once.

(a) Find the probability that these 3 marbles are all red. (Enter your answer as a fraction.)

(b) Find the probability that these 3 marbles are all of the same color. (Enter your answer as a fraction.)

13.

The U.S. Senate consists of 100 members, 2 from each state. A committee of 7 senators is formed. What is the probability that it contains at least one senator from your state? (Round your answer to two decimal places.)

14.

You carry seven keys in your pocket, three of which are for the three locks on your front door. You lose one key. What is the probability that you can get into your house through the front door? (Enter your answer as a fraction.)

15.

Suppose that 80% of drivers are "careful" and 20% are "reckless." Suppose further that a careful driver has a 0.3 probability of being in an accident in a given year, while for a reckless driver the probability is 0.4 What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

16.

Use the given values to find the following. (Enter your answers as fractions.)

17.

A box contains 3 white, 2 red, and black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

18.

You will take either a basket-weaving course or a philosophy course, depending on what your advisor decides. You estimate that the probability of getting an A in basket weaving is 0.80, while in philosophy it is 0.60. However, the chances of your advisor choosing the basket-weaving course is only 10%, while there is a 90% chance that he will put you in the philosophy course. What is the probability that you end up with an A? (Enter your answer to three decimal places.)

19.

Two students are registered for the same class and attend independently of each other, student A 80 0/0 of the time and student B 60 0/0 of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.)

20.

21.

For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

The saddle

The optimal strategy is for R to always choose row and for C to always choose column

22.

23.

24.

25.

26.

Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question.

A farmer grows apples on her 500-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown" produce and her profits per acre increase by $500 if there is no infestation, but they decrease by $100 if there is. If she does use pesticides and there is an infestation, her crop is saved and the resulting apple shortage (since other farms are decimated) raises her profits by $200 per acre. Otherwise, her profits remain at their usual levels.

No worms Worms

No pesticides

Pesticides

How should she divide her farm into a "pesticide-free" zone and a "pesticide-use" zone? (Round your answers to two decimal places.)

The farmer should set aside acres for pesticide-free apples and use pesticide on the other acres.

What will be her expected increase in profits per acre with this strategy?

This strategy will increase her expected profits by $ per acre.