Question 1

A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of 3? 
A) 1
B) 15
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$

Accepted Answer

The even numbers between 1 and 18 are 2, 4, 6, 8, 10, 12, 14, 16, and 18 (9 in total). The multiples of 3 are 3, 6, 9, 12, 15, and 18 (6 in total). However, 6, 12, and 18 are both even and multiples of 3, so they should not be double-counted. Thus, there are 9 (even numbers) + 3 (additional multiples of 3 not already counted as even) = 12 favorable outcomes out of 18 possible outcomes, giving a probability of $\frac{12}{18} = \frac{2}{3}$.

Question 2

An ordinary die is tossed. What are the odds in favor of the die showing a number less than 3?
A) 1 to 3
B) 1 to 1
C) 2 to 1
D) 1 to 2

Accepted Answer

The numbers less than 3 on a die are 1 and 2, so there are 2 favorable outcomes out of 6. The odds in favor are therefore 2 favorable to 4 not favorable, which simplifies to 1 to 2.

Question 3

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 7, or 6? 
A) $\frac { 1 } { 10 }$
B) $\frac { 1 } { 7 }$
C) $\frac { 3 } { 10 }$
D) $\frac { 1 } { 2 }$

Accepted Answer

The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. Here, drawing 2, 7, or 6 are 3 favorable outcomes out of 10 possible outcomes, so the probability is $\frac{3}{10}$.

Question 4

Four boys and three girls are seated, in a row, at random, to watch a play. What is the probability that 
a) a girl is seated at each end of the row?
b) one of the boys is seated in the middle seat?
c) boys and girls are seated alternately? 
A) a) $\frac { 1 } { 7 }$ b) $\frac { 3 } { 7 }$ c) $\frac { 1 } { 35 }$
B) a) $\frac { 1 } { 7 }$ b) $\frac { 4 } { 7 } \quad$ c) $\frac { 1 } { 35 }$
C) a) $\frac { 3 } { 7 }$ b) $\frac { 4 } { 7 }$ c) $\frac { 1 } { 7 }$
D) a) $\frac { 2 } { 7 }$ b) $\frac { 1 } { 7 } \quad$ c) $\frac { 1 } { 35 }$

Accepted Answer

a) To have a girl at each end, we choose 2 girls out of 3 for the ends in $3C2 = 3$ ways, and the remaining 5 can be arranged in $5!$ ways. The total arrangements are $7!$, so the probability is $\frac{3 \times 5!}{7!} = \frac{1}{7}$.b) There are 4 boys, so any one of them can be in the middle seat. The probability is $\frac{4}{7}$ because there are 7 seats and 4 choices for a boy to be in the middle.c) For alternate seating, start with a boy or a girl. There are 2 ways to choose who starts (boy or girl). Then, arrange the boys (4!) and the girls (3!) in their spots. The total is $2 \times 4! \times 3!$, and the probability is $\frac{2 \times 4! \times 3!}{7!} = \frac{1}{35}$.

Question 5

The distribution of B.A. degrees conferred by a local college is listed below, by major. $$\begin{array} { l r } 
\text { Major } & \text { Frequency } \
\hline \text { English } & 2073 \
\text { Mathematics } & 2164 \
\text { Chemistry } & 318 \
\text { Physics } & 856 \
\text { Liberal Arts } & 1358 \
\text { Business } & 1676 \
\text { Engineering } & 868 \
\hline & 9313
\end{array}$$ What is the probability that a randomly selected degree is not in Mathematics?
A) 0.232
B) 0.682
C) 0.768
D) 0.303

Accepted Answer

The total number of degrees is 9313, and the number of degrees in Mathematics is 2164. To find the probability of not selecting a Mathematics degree, subtract the number of Mathematics degrees from the total and then divide by the total: $P(\text{not Mathematics}) = \frac{9313 - 2164}{9313} = \frac{7149}{9313} \approx 0.768$.

Question 6

What are the odds in favor of drawing a number greater than 2 from these cards? 
A) 4 to 5
B) 4 to 1
C) 3 to 5
D) 3 to 2

Accepted Answer

The answer of What are the odds in favor of...

Question 7

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the
Person does not work full time.  1. Public transportation: 6 full time, 7 part time
2. Bicycle: 5 full time, 5 part time
3. Drive alone: 34 full time, 28 part time
4. Car pool: 6 full time, 9 part time
A) 0.51
B) 0.44
C) 0.28
D) 0.49

Accepted Answer

The answer of 100 employees of a company are asked...

Question 8

What is the probability that the arrow will land on 5 or 4? 
A) $\frac { 4 } { 3 }$
B) $\frac { 2 } { 5 }$
C) 5
D) $\frac { 3 } { 5 }$

Accepted Answer

The answer of What is the probability that the arrow...

Question 9

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11? 
A) $\frac { 10 } { 11 }$
B) $\frac { 11 } { 21 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 10 } { 21 }$

Accepted Answer

There are 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) and 1 number 11. The probability is $\frac{11}{21}$.

Question 10

What are the odds in favor of drawing an even number from these cards? 
A) 2 to 3
B) 3 to 2
C) 2 to 5
D) 5 to 2

Accepted Answer

The answer of What are the odds in favor of...

Question 11

If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.04, what are the odds against a direct hit?
A) 23 to 1
B) 24 to 1
C) 1 to 25
D) 25 to 1

Accepted Answer

The answer of If the probability that an identified hurricane...

Question 12

What are the odds in favor of drawing a 4 from these cards? 
A) 5 to 1
B) 1 to 5
C) 1 to 4
D) 4 to 1

Accepted Answer

The answer of What are the odds in favor of...

Question 13

Give the probability that the roll of a die will show 3 or 5. 
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) 2
D) $\frac { 5 } { 6 }$

Accepted Answer

The probability of rolling a 3 or a 5 on a standard six-sided die is $\frac{2}{6}$ because there are two favorable outcomes (rolling a 3 or a 5) out of six possible outcomes. Simplifying $\frac{2}{6}$ gives $\frac{1}{3}$.

Question 14

An ordinary die is tossed. What are the odds in favor of the die showing a 4?
A) 1 to 6
B) 1 to 4
C) 1 to 5
D) 2 to 3

Accepted Answer

The odds in favor of rolling a 4 on a die are 1 to 5, because there is one favorable outcome (rolling a 4) and five unfavorable outcomes (rolling a 1, 2, 3, 5, or 6).

Question 15

If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?
A) 19 to 1
B) 1 to 20
C) 18 to 1
D) 20 to 1

Accepted Answer

The odds against an event are calculated as the ratio of the probability of the event not happening to the probability of the event happening. Here, the probability of not having an earthquake is 1 - 0.05 = 0.95. The odds against an earthquake are therefore 0.95 to 0.05, which simplifies to 19 to 1.

Question 16

One digit from the number 7,212,662 is written on each of seven cards. What is the probability of drawing a card that shows 7, 2, or 1? 
A) $\frac { 3 } { 7 }$
B) $\frac { 4 } { 7 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 5 } { 7 }$

Accepted Answer

The answer of One digit from the number 7,212,662 is...

Question 17

An ordinary die is tossed. What are the odds in favor of the die showing an odd number?
A) 1 to 1
B) 3 to 2
C) 1 to 2
D) 2 to 1

Accepted Answer

There are 3 odd numbers (1, 3, 5) and 3 even numbers (2, 4, 6) on a die, making the odds of rolling an odd number equal to the odds of rolling an even number, which is 1 to 1.

Question 18

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the
Person does not commute by public transportation.  1. Public transportation: 8 full time, 8 part time
2. Bicycle: 5 full time, 3 part time
3. Drive alone: 28 full time, 33 part time
4. Car pool: 9 full time, 6 part time
A) 0.16
B) 1.00
C) 0.42
D) 0.84

Accepted Answer

The answer of 100 employees of a company are asked...

Question 19

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) all are from the same suit?
b) all are hearts?
c) exactly 2 are spades?
A) a) $0.000495$
b) $0.00198$
c) $0.003516$

B) a) $0.00198$
b) $0.000495$
c) $0.27428$

C) a) $0.00198$
b) $0.000495$
c) $0.003516$

D) a) $0.000495$
b) $0.00198$
c) $0.00003$

Accepted Answer

The answer of A 5-card hand is dealt from a...

Question 20

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 8? 
A) $\frac { 13 } { 2 }$
B) 9
C) $\frac { 9 } { 26 }$
D) $\frac { 2 } { 13 }$

Accepted Answer

The answer of A card is drawn from a well-shuffled...

Quiz 7: Arithmetic Sequence: Common Difference and First n Terms

A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of 3?

An ordinary die is tossed. What are the odds in favor of the die showing a number less than 3?

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 7, or 6?

Four boys and three girls are seated, in a row, at random, to watch a play. What is the probability that a) a girl is seated at each end of the row? b) one of the boys is seated in the middle seat? c) boys and girls are seated alternately?

What are the odds in favor of drawing a number greater than 2 from these cards?

What is the probability that the arrow will land on 5 or 4? $What is the probability that the arrow will land on 5 or 4? A) \frac { 4 } { 3 } B) \frac { 2 } { 5 } C) 5 D) \frac { 3 } { 5 }$

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11?

What are the odds in favor of drawing an even number from these cards?

If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.04, what are the odds against a direct hit?

What are the odds in favor of drawing a 4 from these cards?

Give the probability that the roll of a die will show 3 or 5.

An ordinary die is tossed. What are the odds in favor of the die showing a 4?

If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

One digit from the number 7,212,662 is written on each of seven cards. What is the probability of drawing a card that shows 7, 2, or 1?

An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) all are from the same suit? b) all are hearts? c) exactly 2 are spades?

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 8?