Question 1

Solve the problem.
-Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a face card or a black card.

Accepted Answer

In a standard deck, there are 12 face cards (Jacks, Queens, Kings of each suit) and 26 black cards (Spades and Clubs). However, 6 of the black cards are also face cards, so they are counted twice if we simply add these numbers. To avoid double-counting, we calculate the probability as follows: the number of unique cards that are either face cards or black cards is 12 (face cards) + 20 (black non-face cards) = 32. The probability is then 32 out of 52, which simplifies to $\frac{8}{13}$.

Question 2

Solve the problem.
-The final exam grades for a sample of students in a physical science class resulted in the following grade distribution.  If one student taking physical science is selected at random, find the probability of the following events.
a. The student earned an "A".
b. The student earned an "F".

Accepted Answer

The answer of Solve the problem.
-The final exam grades for...

Question 3

Solve the problem.
-Consider the sample space when two fair dice are rolled. Determine the probability for the following event. The sum of the numbers on the dice is not 2.

Accepted Answer

When two fair dice are rolled, there are a total of 6 x 6 = 36 possible outcomes. The only way to get a sum of 2 is by rolling a 1 on both dice, which is just 1 outcome out of the 36. Therefore, the probability of not getting a sum of 2 is 35 out of 36, or $\frac{35}{36}$.

Question 4

Solve the problem.
-A certain city has approximately 2.75 million people. A census indicated that 450,000 people in the city were over the age of 60. If a person is selected at random from the city, what is the probability
That the person is over 60 years old? Round to 3 decimal places.

Accepted Answer

The probability that a randomly selected person is over 60 years old is calculated by dividing the number of people over 60 (450,000) by the total population (2.75 million). This gives 450,000 / 2,750,000 = 0.163636... When rounded to three decimal places, this becomes 0.164.

Question 5

Solve the problem.
-Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a 6 or a queen.

Accepted Answer

There are 4 sixes and 4 queens in a standard deck of 52 cards. Thus, the probability of drawing a 6 or a queen is $\frac{4 + 4}{52} = \frac{8}{52} = \frac{2}{13}$.

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine which of the following can represent the probability of an event?
-$$104 \% , 0.04,0.46 , - \frac { 4 } { 5 }$$

Accepted Answer

Probabilities must be between 0 and 1 (inclusive), so 0.04 and 0.46 are the only valid probabilities.

Question 7

Solve the problem.
-A baseball player with a batting average of 0.304 has a probability of 0.304 of getting a hit for a given time at bat. What is the probability that the player will not get a hit for a given time at bat?

Accepted Answer

The probability of not getting a hit is 1 minus the probability of getting a hit, which is 1 - 0.304 = 0.696.

Question 8

Solve the problem.
-Consider the sample space when two fair dice are rolled. Determine the probability for the following event. The sum of the numbers on the dice is less than 8.

Accepted Answer

The total number of outcomes when two dice are rolled is 36 (6 outcomes for the first die multiplied by 6 outcomes for the second die). The outcomes where the sum is less than 8 are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2), (6,1). This gives us 21 favorable outcomes. Therefore, the probability is 21/36, which simplifies to 7/12.

Question 9

Solve the problem.
-A course in early civilization has 9 freshmen, 8 sophomores, and 12 juniors. If one student is selected at random, find the probability of the following events.
a. A junior is selected.
b. A freshman is selected.
c. A senior is selected.

Accepted Answer

The total number of students is 9 (freshmen) + 8 (sophomores) + 12 (juniors) = 29 students. The probability of selecting a junior is 12/29, a freshman is 9/29, and a senior is 0 since there are no seniors mentioned.

Question 10

Solve the problem.
-At a hospital specializing in treating heart disease, it was found that 224 out of 4,612 patients undergoing open heart mitral valve surgery died during surgery or within 30 days after surgery.
Determine the probability that a patient will not survive the surgery or 30 days after the surgery.
This is called the mortality rate. Round to 3 decimal places.

Accepted Answer

The mortality rate is calculated by dividing the number of patients who died (224) by the total number of patients (4612), which gives 224/4612 = 0.0486. Rounding to three decimal places gives 0.049.

Question 11

Use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event.
-The person has elevated cholesterol. $$\begin{array} { | l | c | c | c | } 
\hline & \begin{array} { c } 
\text { Normal } \
\text { Cholesterol }
\end{array} & \begin{array} { c } 
\text { Elevated } \
\text { Cholesterol }
\end{array} & \text { Total } \
\hline \begin{array} { l } 
\text { 30 and } \
\text { under }
\end{array} & 11 & 5 & 16 \
\hline \mathbf { 3 1 - 6 0 } & 52 & 28 & 80 \
\hline \text { 61 or older } & 24 & 80 & 104 \
\hline \text { Total } & 87 & 113 & 200 \
\hline
\end{array}$$

Accepted Answer

The probability of choosing a person with elevated cholesterol is the number of people with elevated cholesterol divided by the total number of people in the study, which is $\frac{113}{200}$.

Question 12

Solve the problem.
-Suppose that a jury pool consists of 19 women and 20 men. 
a. What is the probability that a jury of 7 people taken at random from the pool will consist only of
Women?
b. What is the probability that the jury will consist only of men?

Accepted Answer

For a, the probability is calculated using combinations: $P(\text{7 women}) = \frac{{\binom{19}{7}}}{{\binom{39}{7}}}$, which approximates to 0.00328. For b, it's $P(\text{7 men}) = \frac{{\binom{20}{7}}}{{\binom{39}{7}}}$, approximating to 0.00504.

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-For two independent events A and B, P(A and
B) = .

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Two events A and B are________ if neither event affects the probability of the other.

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Solve the problem.
-An American roulette wheel has 38 slots, numbered 1 through 36, 0, and 00. Eighteen slots are red, 18 are black, and 2 are green. The dealer spins the wheel in one direction and rolls a small ball in
The opposite direction until both come to rest. The ball is equally likely to fall in any one of the 38
Slots. For a given spin of the wheel, find the 
a. The ball lands on a number that is a multiple of 5 (do not include 0 and 00)
b. The ball does not land on the number 4.

Accepted Answer

Multiples of 5 between 1 and 36 are 5, 10, 15, 20, 25, 30, and 35, totaling 7. The probability is 7 out of 38 slots. For not landing on 4, there are 37 other slots, so the probability is 37 out of 38.

Question 16

Solve the problem.
-Consider an experiment where a die is rolled that has 16 sides. The outcomes are the numbers 1 to 16. Determine the probability of the given event.
A number between 3 and 8, inclusive, is rolled.

Accepted Answer

The answer of Solve the problem.
-Consider an experiment where a...

Question 17

Solve the problem.
-If $P ( E ) = 0.552$, what is the value of $P ( \bar { E } )$ ?

Accepted Answer

The probability of the complement of event E, denoted as $P(\bar{E})$, is calculated as $1 - P(E)$. Given $P(E) = 0.552$, $P(\bar{E}) = 1 - 0.552 = 0.448$.

Question 18

Solve the problem.
-Consider an experiment where a die is rolled that has 15 sides. The outcomes are the numbers 1 to 15. Determine the probability of the given event.
A number less than 4 is rolled.

Accepted Answer

The answer of Solve the problem.
-Consider an experiment where a...

Question 19

Solve the problem.
-Suppose that a student group consists of 10 females and 8 males. What is the probability that a committee of 4 people chosen at random will consist of only females?

Accepted Answer

The probability of choosing a committee of 4 females from a group of 10 females and 8 males is calculated using combinations. The total number of ways to choose 4 people out of 18 is $C(18, 4)$. The number of ways to choose 4 females out of 10 is $C(10, 4)$. The probability is the ratio of these two, which is $\frac{C(10, 4)}{C(18, 4)} = \frac{210}{3060} = 0.0686$, rounding to three decimal places gives 0.069.

Question 20

Solve the problem.
-Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a card numbered between 2 and 10, inclusive or a heart.

Accepted Answer

The answer of Solve the problem.
-Consider the sample space for...

Quiz 8: Sequences, Series, Induction, and Probability

Solve the problem. -Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a face card or a black card.

Solve the problem. -Consider the sample space when two fair dice are rolled. Determine the probability for the following event. The sum of the numbers on the dice is not 2.

Solve the problem. -A certain city has approximately 2.75 million people. A census indicated that 450,000 people in the city were over the age of 60. If a person is selected at random from the city, what is the probability That the person is over 60 years old? Round to 3 decimal places.

Solve the problem. -Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a 6 or a queen.

Choose the one alternative that best completes the statement or answers the question. Determine which of the following can represent the probability of an event? - $104 \% , 0.04,0.46 , - \frac { 4 } { 5 }$

Solve the problem. -A baseball player with a batting average of 0.304 has a probability of 0.304 of getting a hit for a given time at bat. What is the probability that the player will not get a hit for a given time at bat?

Solve the problem. -Consider the sample space when two fair dice are rolled. Determine the probability for the following event. The sum of the numbers on the dice is less than 8.

Solve the problem. -A course in early civilization has 9 freshmen, 8 sophomores, and 12 juniors. If one student is selected at random, find the probability of the following events. a. A junior is selected. b. A freshman is selected. c. A senior is selected.

Solve the problem. -Suppose that a jury pool consists of 19 women and 20 men. a. What is the probability that a jury of 7 people taken at random from the pool will consist only of Women? b. What is the probability that the jury will consist only of men?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -For two independent events A and B, P(A and B) = .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Two events A and B are________ if neither event affects the probability of the other.

Solve the problem. -Consider an experiment where a die is rolled that has 16 sides. The outcomes are the numbers 1 to 16. Determine the probability of the given event. A number between 3 and 8, inclusive, is rolled.

Solve the problem. -If $P ( E ) = 0.552$ , what is the value of $P ( \bar { E } )$ ?

Solve the problem. -Consider an experiment where a die is rolled that has 15 sides. The outcomes are the numbers 1 to 15. Determine the probability of the given event. A number less than 4 is rolled.

Solve the problem. -Suppose that a student group consists of 10 females and 8 males. What is the probability that a committee of 4 people chosen at random will consist of only females?

Solve the problem. -Consider the sample space for a single card drawn from a standard deck. Find the probability that the card drawn is a card numbered between 2 and 10, inclusive or a heart.