The Rules of Probability (Upload) ~ Smart Edition Academy

Which option results in the largest loss on a product?

30% of gaining $2 million and 70% of losing $1 million
60% of gaining $1 million and 40% of losing $2 million
30% of gaining $3 million and 70% of losing $1.5 million
60% of gaining $1.5 million and 40% of losing $2.5 million

Use the following table of the results when rolling two six-sided number cubes.

1, 1	1, 2	1, 3	1, 4	1, 5	1, 6
2, 1	2, 2	2, 3	2, 4	2, 5	2, 6
3, 1	3, 2	3, 3	3, 4	3, 5	3, 6
4, 1	4, 2	4, 3	4, 4	4, 5	4, 6
5, 1	5, 2	5, 3	5, 4	5, 5	5, 6
6, 1	6, 2	6, 3	6, 4	6, 5	6, 6

How many possible outcomes are there for the union of rolling a sum of 3 or a sum of 5?

2
4
6
8

Use the following table of the results when rolling two six-sided number cubes.

1, 1	1, 2	1, 3	1, 4	1, 5	1, 6
2, 1	2, 2	2, 3	2, 4	2, 5	2, 6
3, 1	3, 2	3, 3	3, 4	3, 5	3, 6
4, 1	4, 2	4, 3	4, 4	4, 5	4, 6
5, 1	5, 2	5, 3	5, 4	5, 5	5, 6
6, 1	6, 2	6, 3	6, 4	6, 5	6, 6

How many possible outcomes are there for the intersection of rolling a double and a multiple of 3?

0
2
4
6

Use the following table of the results when rolling two six-sided number cubes.

1, 1	1, 2	1, 3	1, 4	1, 5	1, 6
2, 1	2, 2	2, 3	2, 4	2, 5	2, 6
3, 1	3, 2	3, 3	3, 4	3, 5	3, 6
4, 1	4, 2	4, 3	4, 4	4, 5	4, 6
5, 1	5, 2	5, 3	5, 4	5, 5	5, 6
6, 1	6, 2	6, 3	6, 4	6, 5	6, 6

How many possible outcomes are there for the complement of rolling a 3 and a 5?

16
18
27
36

A deck of cards contains 40 cards divided into 4 colors: red, blue, green, and yellow. Each group has cards numbered 0–9. What is the probability of selecting an 8?

$\frac{1}{10}$
$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{2}$

A deck of cards contains 40 cards divided into 4 colors: red, blue, green, and yellow. Each group has cards numbered 0–9. What is the probability of selecting an even or a red card?

$\frac{1}{4}$
$\frac{3}{8}$
$\frac{5}{8}$
$\frac{3}{4}$

A deck of cards contains 40 cards divided into 4 colors: red, blue, green, and yellow. Each group has cards numbered 0–9. What is the probability of selecting a blue card first, replacing the card, and selecting a 9?

$\frac{1}{100}$
$\frac{1}{80}$
$\frac{1}{40}$
$\frac{1}{20}$

A deck of cards contains 40 cards divided into 4 colors: red, blue, green, and yellow. Each group has cards numbered 0–9. What is the probability of NOT selecting a green card?

$\frac{1}{4}$
$\frac{3}{8}$
$\frac{1}{2}$
$\frac{3}{4}$

What is the expected value of an investment if the probability is $\frac{1}{5}$ of losing $\$1,000$, $\frac{1}{4}$ of no gain, $\frac{2}{5}$ of making $1,000, and $\frac{3}{20}$ of making $2,000?

0
200
500
700

The table below shows the value of the prizes and the probability of winning a prize in a contest.

Prize	$10	$100	$5,000	$50,000
Probability	1 in 50	1 in 1,000	1 in 50,000	1 in 250,000

Calculate the expected value.

$0.10
$0.20
$0.50
$0.60

Which option results in the largest loss on a product?

40% of gaining $100,000 and 60% of losing $100,000
60% of gaining $250,000 and 40% of losing $500,000
30% of gaining $400,000 and 70% of losing $250,000
60% of gaining $250,000 and 40% of losing $450,000

A bag contains 10 red marbles, 8 black marbles, and 7 white marbles. What is the probability of selecting a black marble first and a red marble second with no replacement?

$\frac{8}{25}$
$\frac{16}{125}$
$\frac{2}{15}$
$\frac{7}{75}$

If a letter is chosen at random from the word SUBSTITUTE, what is the probability that the letter chosen is “S” or “T”?

$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$
$\frac{1}{2}$

A spinner contains numbers 1–20. What is the probability of spinning a multiple of 3 or a multiple of 5?

$\frac{3}{10}$
$\frac{1}{5}$
$\frac{9}{20}$
$\frac{11}{20}$

Which option results in the greatest gain on an investment?

100% of gaining $1,000
60% of gaining $2,500 and 40% of gaining $0
75% of gaining $1,000 and 25% of gaining $1,500
70% of gaining $1,500 and 30% of gaining $1,000

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the complement of even cards.

Odd number cards
Even number cards
Green and red cards
Yellow and blue cards

Which option is the greatest gain on a sale?

50% of gaining $8 million and 50% of gaining $7 million
60% of gaining $9 million and 40% of gaining $6 million
70% of gaining $10 million and 30% of gaining $5 million
80% of gaining $11 million and 20% of gaining $4 million

A bag contains 10 red marbles, 8 black marbles, and 7 white marbles. What is the probability of selecting a white marble twice in a row without replacement?

$\frac{7}{100}$
$\frac{49}{600}$
$\frac{14}{25}$
$\frac{343}{600}$

A bucket contains 4 bottles of apple juice, 6 bottles of orange juice, 5 bottles of grape juice, and 10 bottles of water. What is the probability of NOT selecting a bottle of water?

$\frac{1}{5}$
$\frac{2}{5}$
$\frac{3}{5}$
$\frac{4}{5}$

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the union of the first 10 cards.

Green cards
Cards 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Green cards and Red cards; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10

There are 60 students attending classes in town. There are 40 students in dance class and 30 students in art class. Find the number of students in either dance or art class.

30
40
50
60

There are 12 boys’ and 14 girls’ names in a hat. What is the probability of selecting a boy’s name twice in a row without replacement?

$\frac{33}{169}$
$\frac{66}{325}$
$\frac{11}{25}$
$\frac{6}{13}$

A club wants to meet once a week. The available times are Tuesday, Wednesday, and Thursday at 2:00 p.m., 3:00 p.m., and 4:00 p.m. How many outcomes are there for the sample space?

3
6
9
12

Which option results in the greatest gain on an investment?

60% of gaining $5,000 and 40% of gaining $0
70% of gaining $4,500 and 30% of gaining $0
80% of gaining $4,000 and 20% of gaining $0
90% of gaining $3,500 and 10% of gaining $0

Alex and Amir play soccer, Muhammad and David play tennis, and Ji-ho and Frank play both. Describe a union of the people who play soccer or tennis.

Muhammad and David
Ji-ho and Frank
Alex, Amir, Ji-ho, and Frank
Alex, Amir, Muhammad, David, Ji-ho, and Frank

Students were surveyed on if they liked math, social studies, or science as a subject. Describe an intersection of the events.

Students who like math or social studies
Students who like math and social studies
Students who do not like math, social studies, or science
Students who like math

A toy bin contains 12 yellow balls, 3 orange balls, and 5 white balls. What is the probability of selecting an orange or a white ball?

$\frac{3}{80}$
$\frac{3}{20}$
$\frac{1}{4}$
$\frac{2}{5}$

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the intersection of an odd number and blue cards.

Cards 17 and 19
Cards 16, 17, 18, 19, and 20
Cards 11, 13, 15, 17, and 19
Cards 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19

A jar contains 5 red marbles, 15 yellow marbles, 16 blue marbles, 5 purple marbles, and 9 green marbles. What is the probability of selecting a purple or green marble?

$\frac{9}{50}$
$\frac{1}{10}$
$\frac{7}{25}$
$\frac{2}{5}$

The table below shows the value of the prizes and the probability of winning a prize in a contest.

Prize	$5	$100	$10,000	$100,000
Probability	1 in 5	1 in 500	1 in 100,000	1 in 1,000,000

Calculate the expected value.

$1.40
$2.50
$4.00
$5.00

A family has three children. What is the probability that the family has three boys?

$\frac{1}{8}$
$\frac{1}{6}$
$\frac{1}{4}$
$\frac{1}{2}$

A 12-sided number cube is rolled in a game. What is the probability of rolling a 10 or greater on the first roll and a 1 on the second roll?

$\frac{1}{144}$
$\frac{1}{48}$
$\frac{1}{12}$
$\frac{1}{3}$

A cell phone company projects $\frac{1}{2}$ of making $3 million, $\frac{3}{10}$ of making $1 million, and $\frac{1}{5}$ of losing $2 million. What is the expected value?

$1.4 million
$1.5 million
$1.8 million
$2.0 million

A life insurance policy has an annual premium of $600. In case of death, the insurance company will pay $500,000. The probability of dying is 0.0015. What is the expected value after one year?

-750
-150
150
750

Options for lunch are a ham, turkey, or chicken sandwich with chips or pretzels. Identify the sample space.

Pretzels, chips
Ham, turkey, chicken, pretzels, chips
Ham/chips, turkey/chips, chicken/chips
Ham/pretzels, turkey/pretzels, chicken/pretzels, ham/chips, turkey/chips, chicken/chips

A pair of six-sided number cubes is rolled. What is the probability of NOT rolling a sum greater than or equal to 10?

$\frac{1}{6}$
$\frac{1}{3}$
$\frac{2}{3}$
$\frac{5}{6}$

In a board game, a player can continue his turn if he rolls a 5 or 6. Describe the complement of the event.

1
5, 6
1, 2, 3, 4
1, 2, 3, 4, 5, 6

There is a group of 100 people, 68 of whom like hot drinks and 72 of whom like cold drinks. How many people like cold and hot drinks?

4
40
100
140

A spinner is labeled 1–10. What is the probability of landing on a multiple of 3?

$\frac{1}{10}$
$\frac{1}{5}$
$\frac{3}{10}$
$\frac{2}{5}$

The table below shows the value of the prizes and the probability of winning a prize in a state contest.

Prize	$100	$1,000	$10,000	$100,000
Probability	1 in 500	1 in 25,000	1 in 100,000	1 in 2,500,000

Calculate the expected value.

$0.20
$0.38
$0.40
$0.76

The Rules of Probability (Upload)

The Rules of Probability (Upload)

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