Free Printable Rational Equations & Probability Review

1.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

2.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

3.

Solve for d. Simplify your answer.

$\frac{7}{6}d+\frac{3}{4}=-\frac{1}{3}$

a)

$\frac{5}{14}$

b)

$\frac{-13}{14}$

c)

$-1\ \frac{1}{14}$

d)

$1\ \frac{9}{14}$

4.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

5.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

6.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

7.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

8.

What is the probability of the spinner landing on an odd number?

a)

4/8

b)

4/4

c)

1/4

d)

1/3

9.

The two spinners above are spun. What is the probability of getting a perfect square (1,4,9,16), then the letter Z?

a)

3/20

b)

9/20

c)

1/8

d)

11/40

10.

A basket contains four apples and six peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. What is the probability that both pieces of fruit are apples.

a)

2/15

b)

3/17

c)

1/19

d)

6/21

11.

How many ways ways can you arrange 13 people who are waiting in line?

a)

6,227,020,800

b)

13

c)

91

12.

There are 6 meats and 10 veggies available to make a sandwich. How many sandwiches have 3 meats and 5 veggies?

a)

5,020

b)

5,030

c)

5,040

d)

5,050

13.

Welcome to the thrilling game of Deal or No Deal! Isla is in the hot seat, and these are the dollar amounts still in play:

$1,000,000.00

$300,000.00

$50,000.00

$1000.00

$1

The banker has just made an offer of $195,000.00. Based on expected value alone, should Isla take the offer?

a)

No, the expected value is higher, $270,200.20

b)

Yes, the expected value is lower, $170,200.20

c)

No, the expected value is higher, $470,200.20

d)

Yes, the expected value is lower, $190,200.20

14.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

15.

$Solve\ for\ n:\ \frac{3}{5}=\frac{3}{5n}-\frac{1}{5}$

a)

3/5

b)

3/4

c)

1/4

d)

4/5

16.

Solve for n: $\frac{3}{2n}-\frac{3}{2n^2}=\frac{3}{n}$

a)

2

b)

1

c)

-1

d)

-4

17.

\frac{3}{2}+\frac{1}{x}=2

a)

x = 2

b)

x = 7/2

c)

x = -2

d)

x = 4

18.

\frac{3x}{x+1}+\frac{6}{2x}=\frac{7}{x}

a)

$x=\frac{2}{3},-2$

b)

$x=-\frac{2}{3},\ 2$

c)

$x=\frac{3}{2},\ -2$

d)

$x=-\frac{3}{2},\ 2$

19.

\frac{3}{x+4}+\frac{5}{4}=\frac{18}{x+4}

a)

x = 8

b)

x = 16

c)

x = -8

d)

x = -16

20.

Solve

a)

A.

b)

B.

c)

C.

d)

D.

21.

Solve for y $\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}$

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

22.

$\frac{1}{x+8}=\frac{1}{3x+24}+\frac{1}{3}$

a)

$3,\ 8$

b)

$-6$

c)

$\frac{7}{6}$

d)

$3$

23.

$\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}$

a)

$-\frac{23}{5}$

b)

$7$

c)

$-4$

d)

$\frac{4}{3}$

24.

Simplify. (Combine fractions to have like denominators first!)

a)

A

b)

B

c)

C

d)

D

25.

Solve for c. Simplify your answer.

\frac{5}{9}c-\frac{3}{4}=\frac{7}{9}c

a)

$\frac{21}{48}$

b)

$-3\ \frac{3}{8}$

c)

$3\ \frac{3}{8}$

d)

$\frac{27}{8}$

26.

Solve for p. Simplify your answer.
$-\frac{2}{3}p+\frac{8}{3}=3p$

a)

$1\ \frac{1}{7}$

b)

$1\ \frac{3}{11}$

c)

$\frac{8}{7}$

d)

$\frac{8}{11}$

27.

A combination lock has 7 digits. How many distinct combinations does this lock have if the numbers used have to be 0 through 5?

a)

279936

b)

78125

c)

823543

d)

16807

28.

How many ways ways can you arrange the letters in the word math?

a)

15

b)

4

c)

24

29.

In how many ways can 3 different vases be arranged on a tray?

a)

3

b)

9

c)

6

d)

12

30.

Brianna’s school day consists of six classes. How many different ways can her schedule be arranged?

a)

720

b)

36

c)

100

d)

500

31.

Solve for the number of permutations with replacement for the letters X, Y, and Z if each letter can be used more than once.

a)

18

b)

6

c)

12

d)

27

32.

Find the number of permutations without replacement for the letters A, B, C, and D if each letter can only be used once.

a)

12

b)

6

c)

24

d)

10

33.

Determine the number of permutations without replacement for the numbers 1, 2, 3, and 4 if each number can only be used once.

a)

24

b)

8

c)

6

d)

12

34.

Solve for the number of permutations without replacement for the letters X, Y, and Z if each letter can only be used once.

a)

2

b)

3

c)

6

d)

12

35.

How many ways ways can you arrange the letters in the word equation?

a)

40,320

b)

36

c)

8

36.

How many ways ways can you arrange the letters in the word finite?

a)

336

b)

720

c)

6

37.

How many ways ways can you arrange 13 people who are waiting in line?

a)

6,227,020,800

b)

13

c)

91

38.

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

a)

324

b)

4,896

c)

816

d)

54

39.

Six friends are going to play a ball game. Each team has 3 players. How many different team combinations are possible?

a)

120

b)

6

c)

18

d)

20

40.

Kimberly has seven colors of lanyards. She uses three different colors to make a key chain. How many different combinations can she choose?

a)

210

b)

5.040

c)

6

d)

35

41.

How many combinations of 4 letters are possible from the letters A B C D E?

a)

4

b)

5

c)

6

d)

69

42.

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

a)

462

b)

55440

c)

55

d)

1000

43.

Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choose three?

a)

336

b)

56

c)

24

d)

100

44.

If Lucas owns 11 hoodies,how many ways can he choose four to bring on vacation?

a)

44

b)

7920

c)

330

d)

121

45.

Benedic wants to order a sandwich with two of the following ingredients: mushroom, eggplant, tomato, and avocado. How many different sandwiches can Benedic choose?

a)

8

b)

6

c)

4

46.

Four students need to be selected from a class

of 15 to help clean up the campus. How many different ways can the 4 students be chosen?

a)

32 760

b)

60

c)

1 365

47.

If there are 15 dots on a circle, how many triangles can be formed?

a)

445

b)

450

c)

455

d)

460

48.

If there are 17 identified points on a circle, how many lines can be drawn?

a)

136

b)

146

c)

156

d)

166

49.

From a deck of 52 cards, a 5 card hand is dealt. How many distinct 5 card hand are there if the queen of hearts and the eight of spades must be in the hand?

a)

19,400

b)

19,500

c)

19,600

d)

19,700

50.

A lottery has 45 numbers and you must pick 6 numbers. How many different combinations are possible if your lucky numbers 11 and 42 must be on the lottery ticket?

a)

123,380

b)

123,390

c)

123,400

d)

123,410

51.

There are 9 possible toppings for a pizza, but you only want 4 toppings, one of which must be pepperoni. How many different pizzas can be made?

a)

49

b)

56

c)

63

d)

70

52.

If there are 15 pop songs and 12 R&B songs, how many different ways can you select 10 pop songs and 8 R&B songs for your playlist?

a)

1,486,480

b)

1,486,485

c)

1,486,490

d)

1,486,495

53.

How many committees can be formed from 12 men and 10 women if 5 men and 4 women must be on the committee?

a)

166,305

b)

166,310

c)

166,315

d)

166,320

54.

Emma and Daniel are running a quirky insurance company for teenagers! They charge $900 annually for auto policies. The fun part? They promise to pay $1500 for a minor accident and $8000 for a major one. If the probability of a teenager having a minor accident during a given year is 0.15, and of having a major accident is 0.05, how much can Emma and Daniel expect to make on 10 policies?

a)

$275

b)

$625

c)

$2,750

d)

$6,250

55.

Solve for the expected value.

a)

4.5

b)

25.5

c)

3.825

d)

6.52

56.

Kai and Charlotte are playing a game with a magical twelve-sided die!

If they roll a one or a twelve, they win $9.00!

But if they roll any other number less than or equal to nine, they lose $2.00.

And if they roll a number greater than or equal to ten, they lose $1.00. What is the expected value for the host?

a)

$2.00

b)

-$1.00

c)

$0.00 this is a fair game.

d)

$1.50

57.

Join Grace in a thrilling game of Uno! With a deck of 108 cards (25 of each color plus eight wild cards), Grace pays $1.00 to play. If she draws a wild card, she wins $11.00. Can you calculate the expected value for Grace in this exciting game?

a)

Grace loses about 19 cents per play.

b)

Grace wins about 19 cents per play.

c)

Grace loses about 90 cents per play.

d)

Grace wins about 90 cents per play.

58.

Welcome to Lily's Magical Bead Game!

In a jar, there are:

16 orange beads

19 yellow beads

10 pink beads

5 blue beads

Lily picks a bead at random.

If the bead is pink, Lily wins $5.00. If it is blue, she wins $10.00. If it is orange, she pays $3.50. If it is yellow, she pays $2.50. Calculate the expected value for the host.

a)

The host loses 70 cents per game

b)

The host loses 7 cents per game

c)

The host wins 7 cents per game

d)

The host wins 70 cents per game

59.

Paw-some Challenge with Kai and Avery: There are six colorful paw stickers, each a different color: orange, blue, green, purple, yellow, and red, all facing downward. Join Kai and Avery in picking a paw at random! If you pick an AJ color (orange or blue), you win a refreshing coke (value $0.50). If you pick any other color, you pay $1.00. Is this a fair game?

a)

Yes, the expected value is $0

b)

No, the expected value is $0.50

c)

No, the expected value is -$0.50

d)

No, the expected value is -$1.00

60.

Join Abigail and Mason on a thrilling investment adventure! They decide to invest $5000 in Google stocks for five years. Tech stocks have their own rhythm, different from the DJIA. Tech runs and busts dance to their own beat, not following the usual growth-recession cycle. Can you help them calculate the expected value of their investment?

Tech run 2/5 years gain 65%

Tech stable 2/5 years gain 28%

Tech bust 1/5 years lose 38%

What is the expected total of the $5000 investment at the end of the five year run? (Original Investment + Expected Value)

a)

$6480

b)

$8250

c)

$1860

d)

$5000

61.

Emma, the adventurous insurance agent, sells a $250,000.00 life insurance policy to a 28-year-old female in good health for an annual premium of $235.00. A 28-year-old female in good health has a 0.999965 chance of surviving the year. What is the expected value for Emma's company if they sell 1000 such policies in a year?

a)

$87,500

b)

$75,000

c)

$235,000

d)

$226,242

62.

Luna, the inventor, is on a mission to create the ultimate mousetrap! She believes there's a 3/4 chance that her new design will be a hit. If successful, it will bring in a whopping $120,000. However, the development costs are $98,000. What is Luna's expected gain or loss from this venture?

a)

Loss $65,500

b)

Gain $65,500

c)

Loss $74,000

d)

Gain $74,000

63.

Michael just bought a cozy little house and decided to take out a fire insurance policy. The annual premium is $300. In case of a fire, the insurance company will pay him $200,000. The probability of a house fire in his area is 0.0002.

What is Michael's expected value from this insurance policy?

a)

$199,660

b)

-$199,660

c)

-$260

d)

$260

64.

Elijah, the car dealer, is on a mission to save the planet by selling hybrid cars! He buys each hybrid for $21,000 and sells them for $24,500. With his trusty sidekick, Kai, they track their weekly sales. Can you help them calculate their expected weekly profit?

a)

$2,380

b)

$5,355

c)

$6,475

d)

$5,075

65.

Mia and Ethan are playing a fun coin-toss game at the school fair! They toss three fair coins. If all land "heads," they win $10, and if exactly two land heads, they win $5. But it costs $4 to play. What is the expected outcome of the game for them?

(Hint: use combinations to determine the number of combinations that land heads twice.)

a)

Loss of $1.125

b)

Loss of $2.875

c)

Win of $1.125

d)

Win of $2.875

66.

Noah, Benjamin, and Luna are part of a student group that sells 500 raffle tickets for $2 each to raise funds for their school trip. At the exciting raffle draw, the top prize is a $100 gift certificate to the coolest local store. The second prize is a $50 gift card, and there are five thrilling 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average) in this fun raffle? How much?

a)

lose an average of $5.50

b)

lose an average of $1.50

c)

win an average of $2.00

d)

lose an average of $10.00

67.

Michael and Elijah are playing a thrilling game with a magical die that has three red sides, two green sides, and one blue side. Rolling a red means a loss, rolling a green wins you $2.00, and rolling a blue wins you $5.00. The entry fee to join this exciting game is $2.00. What is the expected value of playing this game?

a)

$0

b)

-$0.50

c)

$.67

d)

$-1.50

68.

Your friend Arjun, a master card trickster, shuffles a standard deck of cards with a flourish and challenges you to a game. If you draw a face card (Jack, Queen, King of each suit), Arjun will reward you with $10. However, if you draw any other card, you'll owe Arjun $5. How much should you expect to win or lose by playing this intriguing game?

a)

Lose $6.15

b)

Win $6.15

c)

Lose $1.54

d)

Win $1.50

69.

Benjamin, the adventurous stockbroker, is predicting the future of his favorite stock. He believes there's a 40% chance it will soar to $50, a 35% chance it will climb to $60, and a 25% chance it will reach $70 by the year's end.
What magical expected value does Benjamin assign to this stock's end-of-the-year price?

a)

$58.50

b)

$60.00

c)

$62.50

d)

$65.00

70.

Solve!

a)

x = 4

b)

x = -5

c)

x = 5.4

d)

x = 6

71.

Solve!

a)

x = 36/7

b)

x = 6

c)

x = 44/7

d)

x = 0

Rational Equations & Probability Review

Total questions: 71

Worksheet time: 2hrs 49mins

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