Mathematics homework help

Borough of Manhattan Community College

Mathematics Department

Name___________________________ Instructor L. Erstenyuk

Date ___________________________ MAT 216-_____________

EXAM 1 REVIEW

Instructions. Show all steps and label answers. Papers will be graded on clarity, neatness

and organization as well as correctness. You may use a regular scientific calculator during

the exam.

1. Create a tree diagram to represent the possible combinations of outfits for a school

dress code. The pants must be either navy or tan and the shirts must be white, red, or

blue.

2. Create a product table illustrating the possible outcomes of rolling two four-sided dice

(with numbers 1 – 4). Then answer the questions.

a.) List the ways that both dice are show even numbers?

b.) What is the probability that both dice are showing even numbers?

c.) What is the probability the sum of the dice is at most seven?

d.) What are the odds in favor of the dice summing to at most seven?

Die 1 (down),

Die 2 (across)

Evaluate without using a calculator.

3. 4!

4. 6!

5.
10!

8!

6.
12!

9! ∙ 3!

7. How many odd four-digit numbers exist in our Hindu-Arabic number system?

8. How many odd four-digit numbers that do not contain the digits 2 or 4 exist in our Hindu-

Arabic number system?

9. The town of Holmdel, NJ has three prefixes (the first three digits of a 7-digit phone

number), 946, 739, and 264. Assuming no other restrictions, how many phone numbers

can be given to residents of Holmdel?

10. Write the formula, substitute, then evaluate:

a) ⬚13𝑃3

b) ⬚21𝐶18

11. The Stand Up Comedy Club at Webber College has 6 members:

{Abe, Bart, Carl, Homer, Lisa, Marge}

ai.) How many ways could they be ordered for a show?

aii.) What is the probability the first comedian will be female?

bi.) How many ways could two people be chosen to attend a Laugh-a-Minute workshop?

bii.) What is the probability the two people chosen for the workshop are both male?

12. How many different Golf hands could be dealt from a standard deck of 52 cards if in

the game of Golf each player receives 4 cards?

13. Utah’s license plates have two letters followed by three numbers followed by another

letter. How many possible combinations of Utah license plates exist (before not

allowing inappropriate plates)?

14. Find the number of distinguishable arrangements of the letters of the word

HAVANNAH.

15. Refer to Pascal’s Triangle. Suppose seven fair coins are tossed.

a) How many ways could the 7 coins land total?

b) Find the number of ways there could be exactly two heads.

c) What is the probability exactly two coins will land on heads?

d) What is the probability that at least two coins will land on heads?

16. Consider the standard deck of 52 cards.

a) If a single card is chosen from the deck, what is the probability it will be a ten or a

red card?

b) If two cards are dealt from a deck of cards, then what is the probability they will

both be face cards?

17. If an integer is chosen at random from 1 – 38, what is the probability it is a multiple

of 3 or a multiple of 4?

18. There are 9 black, 6 navy, and 5 green marbles in a bag. One marble is chosen at

random and its color is recorded. A second marble is drawn and its color is recorded.

Create a probability tree representing this information.

a) What is the probability of choosing two green marbles?

b) What is the probability at least one marble is black?

c) What is the probability of selecting one navy marble and one black marble (in either

order, that is, navy then black or black then navy)?

d) What is the probability neither marble is black?

19. The owner of a restaurant serving Continental-style entrees was interested in studying

ordering patterns of patrons for the Friday-to-Sunday weekend time period. Records

were maintained that indicated the demand for dessert during the same period of time:

DEMAND FOR DESSERT

Desert Ordered Male Female Total

Yes 96 40 136

No 224 240 464

Total 320 280 600

A waiter approaches a table to take an order. What is the probability that the first customer to

order at the table:

a) Orders a dessert?

b) Is a male?

c) Is a female and does not order a dessert?

d) Is a female or does not order a dessert?

e) Orders a dessert given a customer is a female?

20. Use the binomial formula to compute the following probability:

𝑛 = 7, 𝑝 = 0.6, 𝑥 = 4.

21. A 35-year-old woman purchases a $100,000 term life insurance policy for an annual

payment of $360. Based on a period life table for the U.S. government, the

probability that she will survive the year is 0.999057. Find the expected value of the

policy for the insurance company.