Question 1

Probability
1 Compute Empirical Probability
-The table below represents the number of deaths per 100 cases for an illness having a median mortality of four years and a right-skewed distribution over time. What is the probability of living more than 12 years after diagnosis of the disease?

A) $15.00 \%$
B) $19.00 \%$
C) $13.00 \%$
D) $85.00 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-The table below represents...

Question 2

Compute Theoretical Probability
-A 6-sided die is rolled. What is the probability of rolling a number less than 3 ?
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 6 }$

Accepted Answer

Numbers less than 3 on a 6-sided die are 1 and 2, so there are 2 favorable outcomes out of 6 possible outcomes, giving a probability of $\frac{2}{6}$ which simplifies to $\frac{1}{3}$.

Question 3

Find the Probability that an Event Will Not Occur
-What is the probability that a card drawn from a deck of 52 cards is not a heart?
A) $\frac { 3 } { 4 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 4 } { 13 }$
D) $\frac { 2 } { 5 }$

Accepted Answer

In a deck of 52 cards, there are 13 hearts. Therefore, the probability of drawing a heart is $\frac{13}{52} = \frac{1}{4}$. The probability of not drawing a heart is $1 - \frac{1}{4} = \frac{3}{4}$.

Question 4

Additional Concepts
-$\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$
A) $- 2249$
B) 2249
C) $- 2345$
D) $- 41$

Accepted Answer

The expression simplifies as follows: $\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$ can be simplified step by step. First, calculate the combinations and the factorial fractions:${ } _ { 7 } C _ { 3 } = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$${ } _ { 5 } C _ { 1 } = \frac{5!}{1!(5-1)!} = \frac{5}{1} = 5$So, the first part of the expression becomes $\frac{35}{5} = 7$.For the second part:$\frac { 48 ! } { 46 ! } = \frac{48 \times 47 \times 46!}{46!} = 48 \times 47 = 2256$Putting it all together:$7 - 2256 = -2249$

Question 5

Compute Theoretical Probability
-A bag contains 5 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
A) $\frac { 6 } { 13 }$
B) $\frac { 5 } { 13 }$
C) $\frac { 2 } { 13 }$
D) $\frac { 6 } { 11 }$

Accepted Answer

The total number of marbles is 5 + 6 + 2 = 13. The probability of choosing a blue marble is the number of blue marbles divided by the total number of marbles, which is $\frac{6}{13}$.

Question 6

Probability
1 Compute Empirical Probability
-In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?

A) $22.40 \%$
B) $28.66 \%$
C) $23.59 \%$
D) $28.76 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-In 1999 the stock...

Question 7

Compute Theoretical Probability
-A lottery game contains 24 balls numbered 1 through 24 . What is the probability of choosing a ball numbered 25?
A) 0
B) 1
C) $\frac { 1 } { 24 }$
D) 24

Accepted Answer

Since there are no balls numbered 25 in the set of balls numbered 1 through 24, the probability of choosing a ball numbered 25 is 0.

Question 8

Compute Theoretical Probability
-A bag contains 17 balls numbered 1 through $17 .$ What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?
A) $\frac { 8 } { 17 }$
B) $\frac { 17 } { 8 }$
C) $\frac { 2 } { 17 }$
D) 8

Accepted Answer

There are 8 even numbers (2, 4, 6, 8, 10, 12, 14, 16) out of 17 total numbers, so the probability is $\frac{8}{17}$.

Question 9

Additional Concepts
-$\frac{5 C_{3} \cdot 4^{C}}{16 C_{13}}$

A) $\frac { 1 } { 14 }$
B) $\frac { 1 } { 7 }$
C) $\frac { 1 } { 56 }$
D) $\frac { 15 } { 14 }$

Accepted Answer

The answer of Additional Concepts
-$\frac{5 C_{3} \cdot 4^{C}}{16 C_{13}}$

A) \(\frac...

Question 10

Compute Theoretical Probability
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3 ?
A) $\frac { 1 } { 18 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 17 } { 18 }$
D) 2

Accepted Answer

The sum of 3 can be achieved only with the combinations (1,2) and (2,1) out of the 36 possible outcomes (6 options for the first die times 6 options for the second die), which gives a probability of $\frac{2}{36} = \frac{1}{18}$.

Question 11

Compute Theoretical Probability
-A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
A) $\frac { 4 } { 5 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 1 } { 5 }$
D) 8

Accepted Answer

The total number of marbles is 10 (7 red + 2 blue + 1 green). The probability of not choosing a blue marble is the number of marbles that are not blue (which is 8) divided by the total number of marbles, giving $\frac{8}{10}$ which simplifies to $\frac{4}{5}$.

Question 12

Probability
1 Compute Empirical Probability
-During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 12.3 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a thunderstorm?
A) 60.32%
B) 59.00%
C) 39.68%
D) 87.70%

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-During July in Jacksonville,...

Question 13

Probability
1 Compute Empirical Probability
-During clinical trials of a new drug intended to reduce the risk of heart attack, the following data indicate the occurrence of adverse reactions among 1000 adult male trial members. What is the probability that an adult male using the drug will experience nausea?

A) $2.50 \%$
B) $28.09 \%$
C) $2.30 \%$
D) $1.70 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-During clinical trials of...

Question 14

Probability
1 Compute Empirical Probability
-Use of the internet for shopping is increasing dramatically, but still is somewhat age dependent. When a popular web site that sells books asked the age of users who bought products from them over the internet they obtained the following data. What is the probability that a buyer on this web site is aged $60 - 69$ ?

A) $2.27 \%$
B) $3.14 \%$
C) $3.16 \%$
D) $2.32 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-Use of the internet...

Question 15

Probability
1 Compute Empirical Probability
-Measurements of the height of a group of men entering a particular college produced the following table. What is the probability that a man entering the college is 68-69 inches tall?

A) $29.22 \%$
B) $23.27 \%$
C) $21.04 \%$
D) $29.47 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-Measurements of the height...

Question 16

Find the Probability that an Event Will Not Occur
-A bag contains 3 blue marbles, 8 green marbles, and 5 red marbles. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?
A) $\frac { 13 } { 16 }$
B) $\frac { 3 } { 13 }$
C) $\frac { 3 } { 16 }$
D) $\frac { 13 } { 3 }$

Accepted Answer

The total number of marbles is 3 (blue) + 8 (green) + 5 (red) = 16. The probability of not drawing a blue marble is the probability of drawing either a green or a red marble, which is 8 + 5 = 13 out of 16, or $\frac{13}{16}$.

Question 17

Probability
1 Compute Empirical Probability
-A traffic engineer is counting the number of vehicles by type that turn into a residential area. The table below shows the results of the counts during a four-hour period. What is the probability that the next vehicle passing is an SUV?

A) $30.95 \%$
B) $20.68 \%$
C) $32.46 \%$
D) $31.46 \%$

Accepted Answer

The answer of Probability
1 Compute Empirical Probability
-A traffic engineer is...

Question 18

Compute Theoretical Probability
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?
A) $\frac { 1 } { 6 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 12 }$
D) 6

Accepted Answer

The sums greater than 9 are achieved with the following pairs: (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). There are 6 favorable outcomes out of 36 possible outcomes (each die has 6 sides, so 6*6 = 36 total outcomes), giving a probability of $\frac{6}{36} = \frac{1}{6}$.

Question 19

Find the Probability that an Event Will Not Occur
-What is the probability that a card drawn from a deck of 52 cards is not red?
A) $\frac { 1 } { 2 }$
B) 2
C) $\frac { 25 } { 52 }$
D) $\frac { 3 } { 4 }$

Accepted Answer

The probability that a card drawn is not red is the same as the probability that the card drawn is black. Since there are 26 black cards in a deck of 52 cards, the probability is $\frac{26}{52} = \frac{1}{2}$.

Question 20

Find the Probability that an Event Will Not Occur
-What is the probability that a card drawn from a deck of 52 cards is not a 2 ?
A) $\frac { 12 } { 13 }$
B) $\frac { 1 } { 13 }$
C) $\frac { 9 } { 10 }$
D) $\frac { 1 } { 10 }$

Accepted Answer

The probability that a card drawn is not a 2 is 1 minus the probability of drawing a 2. Since there are 4 twos in a 52-card deck, the probability of drawing a 2 is $\frac{4}{52} = \frac{1}{13}$. Therefore, the probability of not drawing a 2 is $1 - \frac{1}{13} = \frac{12}{13}$.

Quiz 11: Sequences, Induction, and Probability

Compute Theoretical Probability -A 6-sided die is rolled. What is the probability of rolling a number less than 3 ?

Find the Probability that an Event Will Not Occur -What is the probability that a card drawn from a deck of 52 cards is not a heart?

Additional Concepts - $\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$

Compute Theoretical Probability -A bag contains 5 red marbles, 6 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Compute Theoretical Probability -A lottery game contains 24 balls numbered 1 through 24 . What is the probability of choosing a ball numbered 25?

Compute Theoretical Probability -A bag contains 17 balls numbered 1 through $17 .$ What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Additional Concepts - $\frac{5 C_{3} \cdot 4^{C}}{16 C_{13}}$

Compute Theoretical Probability -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3 ?

Compute Theoretical Probability -A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Probability 1 Compute Empirical Probability -During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 12.3 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a thunderstorm?

Find the Probability that an Event Will Not Occur -A bag contains 3 blue marbles, 8 green marbles, and 5 red marbles. One marble is drawn from the bag. What is the probability that the marble drawn is not blue?

Compute Theoretical Probability -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?

Find the Probability that an Event Will Not Occur -What is the probability that a card drawn from a deck of 52 cards is not red?

Find the Probability that an Event Will Not Occur -What is the probability that a card drawn from a deck of 52 cards is not a 2 ?

Quiz 11: Sequences, Induction, and Probability

Probability 1 Compute Empirical Probability -The table below represents the number of deaths per 100 cases for an illness having a median mortality of four years and a right-skewed distribution over time. What is the probability of living more than 12 years after diagnosis of the disease?