Deck 9: Sequences, Series, and Probability

Question 1

Find the probability of tossing a coin 7 times and getting exactly one head.

A)
B)
C)
D)

Answer 1

Question 2

Find the probability of tossing 7 coin a times and getting exactly 6 tails.

A)
B)
C)
D)

Answer 2

Question 3

Find the probability for the experiment of selecting a single card from a deck of 52 cards and have it be a 2, 7, or 10.

A)
B)
C)
D)

Answer 3

Question 4

Find the probability for the experiment of selecting a single card from a deck of 52 cards and have it be a spade.

A)
B)
C)
D)

Question 5

Find the probability for the experiment of selecting a single card from a deck of 52 cards and have it be an even number.

A)
B)
C)
D)

Question 6

Find the probability of E not occurring if P(E) = .

A) 1
B)
C) 0
D)

Question 7

Find the probability of either or occurring if and are mutually exclusive and, and

A)
B)
C)
D)

Question 8

Find the probability of tossing a coin 2 times and getting exactly 2 heads. Express the answer as a decimal.

Question 9

Find the probability of not occurring if

Question 10

What is the probability that of six children at least one is a girl?

A) 0.1875
B) 0.984375
C) 0.015625
D) 0.09375

Question 11

Find the probability of rolling a 5 on a 6-sided die.

Question 12

Find the probability of tossing two die and rolling a sum of 10.

Question 13

Find the probability of tossing two die and rolling a sum that is less than 9.

Question 14

Find the probability of either or occurring if P( ) = and and and are not mutually exclusive and

Question 15

Use the formula for to evaluate .

A) 30,240
B) 252
C) 50
D) 90

Question 16

Use the formula for to evaluate .

A) 108,900
B) 77
C) 330
D) 1,663,200

Question 17

Use the formula for to evaluate .

A) 0
B) 1
C) 10
D) 3,628,800

Question 18

Use the formula for to evaluate .

A) 0
B) 1
C) 4
D) 24

Question 19

Use the formula for to evaluate .

A) 165
B) 88
C) 6,652,800
D) 990

Question 20

Use the formula for to evaluate .

A) 220
B) 79,833,600
C) 108
D) 23,760

Question 21

Use the formula for to evaluate .

A) 0
B) 1
C) 17
D) 33

Question 22

Use the formula for to evaluate .

A) 0
B) 1
C) 10
D) 9

Question 23

Use the formula for to evaluate .

A) 4536
B) 3024
C) 36
D) 126

Question 24

At Marcello's Pizza restaurant, there are 5 types of crust, 2 types of cheese, and 10 types of toppings to choose from. How many different pizzas can be made from one type of crust, one type of cheese, and one topping?

A) 17
B) 100
C) 252
D) 45

Question 25

At Point Loma Soup and Salad restaurant, there are 4 types of lettuce, 8 types of salad ingredients, and 5 different dressings to choose from. How many different salads can be made from one type of lettuce, one salad ingredient, and one dressing?

A) 6720
B) 17
C) 160
D) 70

Question 26

Use the formula for to evaluate .

Question 27

Use the formula for to evaluate .

Question 28

In a deck of 52 cards, how many different 3-card hands can be dealt?

Question 29

If a state lottery picks from 59 numbers and 4 numbers are selected, how many possible 4-number combinations are there?

Question 30

A safe will open when the correct choice of three numbers (1 to 51) is selected and entered in the correct order. How many possible permutations are there, assuming no numbers can be repeated?

Question 31

In a particular state there are seven characters in a license plate: three letter(s) followed by four numbers. If 0s and 1s are eliminated from possible numbers and Os and Is are eliminated from possible letters, how many different license plates can be made?

A) 78,624,000
B) 20,401,920
C) 141,680
D) 546,000

Question 32

Use the formula for to evaluate .

Question 33

Use the formula for to evaluate .

Question 34

Use the formula for to evaluate .

Question 35

Use the formula for to evaluate .

Question 36

Use the formula for to evaluate .

Question 37

Use the formula for to evaluate .

Question 38

Use the formula for to evaluate .

Question 39

Use the formula for to evaluate .

Question 40

Use the formula for to evaluate .

Question 41

Evaluate the binomial coefficient .

A) 35
B) 840
C) 3.5
D) 21

Question 42

Evaluate the binomial coefficient .

A) 10,897,286,400
B) 3003
C) 75
D) 600.6

Question 43

Evaluate the binomial coefficient .

A) 1092
B) 176
C) 4368
D) 48,048

Question 44

Evaluate the binomial coefficient .

A) 767,240.81
B) 1,160,068,104
C) 1548
D) 32,224,114

Question 45

Evaluate the binomial coefficient .

A) 79,833,600
B) 220
C) 108
D) 1980

Question 46

Expand using the binomial theorem.

A)
B)
C)
D)

Question 47

Expand using the binomial theorem.

A)
B)
C)
D)

Question 48

Expand using the binomial theorem.

A)
B)
C)
D)

Question 49

Expand using Pascal's Triangle.

A)
B)
C)
D)

Question 50

Expand using Pascal's Triangle.

A)
B)
C)
D)

Question 51

Find the coefficient, C, of the term in the binomial expansion.

A) 8
B) 2016
C) 144
D) 672

Question 52

Find the coefficient, C, of the term in the binomial expansion.

A) -1280
B) 1280
C) 64
D) -64

Question 53

Find the coefficient, C, of the term in the binomial expansion.

A) 84,375
B) 3152
C) 30,375
D) 4,725,000

Question 54

Find the coefficient, C, of the term in the binomial expansion.

A) 324
B) -324
C) 81
D) -81

Question 55

Expand the binomial coefficient.

Question 56

Expand using the binomial theorem.

Question 57

In a state lottery in which 5 numbers are drawn from a possible 40 numbers, the number of possible 5 number combinations is equal to: How many possible combinations are there?

Question 58

Expand the expression using the binomial theorem.

A)
B)
C)
D)

Question 59

Expand the expression using the binomial theorem.

A)
B)
C)
D)

Question 60

Evaluate the binomial coefficient .

Question 61

Evaluate the binomial coefficient .

Question 62

Evaluate the binomial coefficient .

Question 63

Evaluate the binomial coefficient .

Question 64

Evaluate the binomial coefficient .

Question 65

Expand using the binomial theorem.

Question 66

Expand using the binomial theorem.

Question 67

Expand using the binomial theorem.

Question 68

Expand using Pascal's Triangle.

Question 69

Expand using Pascal's Triangle.

Question 70

Find the coefficient, C, of the term in the binomial expansion.

Question 71

Find the coefficient, C, of the term in the binomial expansion.

Question 72

Find the coefficient, C, of the term in the binomial expansion.

Question 73

Find the coefficient, C, of the term in the binomial expansion.

Question 74

Prove the statement using mathematical induction for all positive integers, n.≤

Question 75

Prove the statement using mathematical induction for all positive integers, n.<

Question 76

Prove the statement using mathematical induction for all positive integers, n.8 + 13 + 18 + ... + (5n + 3) = n(5n + 11)/2

Question 77

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + = ( - 1)/8

Question 78

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + = 1 -

Question 79

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + =

Question 80

Prove the statement using mathematical induction for all positive integers, n. n(n + 1)(n + 2) is divisible by 3