Assignment Prompt & Instructions
I need support with a math question. I will attach the document for review.
– ## math216week2hw.pdf
**## math216week2hw.pdf**
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)
Yvonne Logan
6/4/25
Red shirt
white shirt
blue shirt
Navy pants
tan pants
Navy pants
tan pants
navy pants
tan pants
1
2
3
4
1
2
3
4
2
4
6
8
3
4
5
3
4
5
5
6
5
7
6
7
( 2,2) (4,4)
50% because there are an equal amount of even and odd numbers
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?
4x3x2x1
=24
6x5x4x3x2x1
=720
10x9x /8!
8!
10 x 9 = 90
12 x 11 x 10 9 x 8 x 7 x 6 x 5 x4 3!
9! x 3!
79,833,600
362,880
220
four digit A, B, C, D must be odd 1, 3, 5, 7, 9
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?
p( n,r)= n!
(n-r)!
13!
(13-3) !
21!
18! 3!
2 female
4 males
6 total members
2 female
4 males
6 total members
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.
E company premium – payout
**## math216week2hw.pdf**
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)
Yvonne Logan
6/4/25
Red shirt
white shirt
blue shirt
Navy pants
tan pants
Navy pants
tan pants
navy pants
tan pants
1
2
3
4
1
2
3
4
2
4
6
8
3
4
5
3
4
5
5
6
5
7
6
7
( 2,2) (4,4)
50% because there are an equal amount of even and odd numbers
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?
4x3x2x1
=24
6x5x4x3x2x1
=720
10x9x /8!
8!
10 x 9 = 90
12 x 11 x 10 9 x 8 x 7 x 6 x 5 x4 3!
9! x 3!
79,833,600
362,880
220
four digit A, B, C, D must be odd 1, 3, 5, 7, 9
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?
p( n,r)= n!
(n-r)!
13!
(13-3) !
21!
18! 3!
2 female
4 males
6 total members
2 female
4 males
6 total members
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.
E company premium – payout