Question 1

Provide an appropriate response.
-Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is
Replaced before the second card is drawn.

Accepted Answer

The events are independent because the first ace being drawn and replaced does not affect the likelihood of drawing another ace on the second draw. The probability of drawing an ace on the first draw is 4/52, and the probability of drawing an ace on the second draw is also 4/52, regardless of what card was drawn on the first draw. Therefore, the events are independent. The events of getting two aces are independent because the first ace being drawn and replaced before the second card is drawn does not affect the probability of getting another ace on the second draw. The probability of getting an ace on the first draw is 4/52 or 1/13. Since the first ace is replaced, the probability of getting another ace on the second draw is still 1/13. The events are independent because the occurrence of the first event does not affect the probability of the second event.

Question 2

Provide an appropriate response.
-Classify the events as dependent or independent. Events A and B where P(A)= 0.8, P(B)= 0.2, and P(A and B)= 0.16

Accepted Answer

Events A and B are independent because the product of their individual probabilities, P(A) * P(B) = 0.8 * 0.2 = 0.16, equals the probability of both events happening together, P(A and B).

Question 3

Provide an appropriate response.
-Classify the statement as an example of classical probability, empirical probability, or subjective probability. In California?s Pick Three lottery, a person selects a 3-digit number. The probability of winning California?s
Pick Three lottery is $\frac { 1 } { 1000 }$

Accepted Answer

Classical probability is used when all outcomes are equally likely, as in the case of a lottery where each 3-digit number has an equal chance of being drawn.

Question 4

Provide an appropriate response.
-A group of students were asked if they carry a credit card. The responses are listed in the table. $$\begin{array} { l | c | c | c } 
 { \text { Class } } & \begin{array} { c } 
\text { Credit Card } \
\text { Carrier }
\end{array} & \begin{array} { c } 
\text { Not a Credit Card } \
\text { Carrier }
\end{array} & \text { Total } \
\hline \text { Freshman } & 40 & 20 & 60 \
\text { Sophomore } & 25 & 15 & 40 \
\text { Total } & 65 & 35 & 100
\end{array}$$ If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

Accepted Answer

The probability that a randomly selected student owns a credit card given that the student is a freshman is calculated by dividing the number of freshmen who own a credit card by the total number of freshmen. This is $ \frac{40}{60} = 0.667 $.

Question 5

Provide an appropriate response.
-At the local racetrack, the favorite in a race has odds 3:2 of losing. What is the probability that the favorite wins the race?

Accepted Answer

The answer of Provide an appropriate response.
-At the local racetrack,...

Question 6

Write the word or phrase that best completes each statement or answers the question
-Explain why the following statement is incorrect:
He gave 110% effort.

Accepted Answer

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

Question 7

Provide an appropriate response.
-A group of students were asked if they carry a credit card. The responses are listed in the table. $$\begin{array} { l | c | c | c } 
 { \text { Class } } & \begin{array} { c } 
\text { Credit Card } \
\text { Carrier }
\end{array} & \begin{array} { c } 
\text { Not a Credit Card } \
\text { Carrier }
\end{array} & \text { Total } \
\hline \text { Freshman } & 28 & 32 & 60 \
\text { Sophomore } & 10 & 30 & 40 \
\text { Total } & 38 & 62 & 100
\end{array}$$ If a student is selected at random, find the probability that he or she is a sophomore and owns a credit card. Round your answers to three decimal places.

Accepted Answer

The probability that a randomly selected student is a sophomore and owns a credit card is calculated by dividing the number of sophomores who own a credit card (10) by the total number of students (100), which equals 0.100.

Question 8

Write the word or phrase that best completes each statement or answers the question.
-You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places.

Accepted Answer

The probability of drawing a two from a standard deck of 52 playing cards is 4/52, or 1/13. Since the first card is not replaced, the probability of drawing a ten as the second card is 4/51, since there are now only 51 cards left in the deck. To find the probability of both events happening, we need to multiply the probabilities. Therefore, (1/13) * (4/51) = 4/663, which when rounded to three decimal places is 0.006. So the correct answer is choice letter A. The probability of drawing a two on the first card is 4/52 (there are four twos in a deck of 52 cards). The probability of drawing a ten on the second card, given that the first card was a two, is 4/51 (there are four tens left in a deck of 51 cards). Therefore, the probability of both events occurring in succession is (4/52)*(4/51) = 0.006.

Question 9

Provide an appropriate response.
-Classify the events as dependent or independent. Event A: A red candy is selected from a package with 30 colored candies and eaten. Event B: A blue candy is selected from the same package and eaten.

Accepted Answer

Event A and B are dependent because the selection of a red candy in Event A affects the number of candies and colors remaining in the package for Event B. If a red candy is selected in Event A, then there are fewer candies and colors left in the package, making it less likely that a blue candy will be selected in Event B.

Question 10

Provide an appropriate response.
-Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is not replaced before the second card is drawn.

Accepted Answer

The events are dependent because the probability of getting a second ace is affected by the removal of the first ace from the deck. If the first card drawn is an ace, the probability of getting a second ace is reduced because there is one less ace in the deck. Therefore, the occurrence of the first event affects the probability of the second event. The events are dependent because the probability of getting an ace on the second draw is dependent on whether or not an ace was already drawn on the first draw. If an ace was already drawn, there is one less ace in the deck and therefore a lower probability of getting another ace on the second draw.

Question 11

Write the word or phrase that best completes each statement or answers the question.
-Find the probability of answering two true or false questions correctly if random guesses are made. Only one of the choices is correct.

Accepted Answer

The probability of guessing one question correctly is 0.5 (since there are two options, true or false, making the chance of a correct guess 1 out of 2). For two questions, you multiply the probabilities: 0.5 * 0.5 = 0.25.

Question 12

Provide an appropriate response.
-A group of students were asked if they carry a credit card. The responses are listed in the table. $$\begin{array} { l | c | c | c } 
 { \text { Class } } & \begin{array} { c } 
\text { Credit Card } \
\text { Carrier }
\end{array} & \begin{array} { c } 
\text { Not a Credit Card } \
\text { Carrier }
\end{array} & \text { Total } \
\hline \text { Freshman } & 11 & 49 & 60 \
\text { Sophomore } & 6 & 34 & 40 \
\text { Total } & 17 & 83 & 100
\end{array}$$ If a student is selected at random, find the probability that he or she owns a credit card given that the student is a sophomore. Round your answer to three decimal places.

Accepted Answer

The answer of Provide an appropriate response.
-A group of students...

Question 13

Provide an appropriate response.
-Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a newborn baby is a boy iis $\frac { 1 } { 2 }$

Accepted Answer

Classical probability is used when all outcomes are equally likely, such as flipping a coin or, in this case, the equally likely chance of a newborn being a boy or a girl.

Question 14

Provide an appropriate response.
-A group of students were asked if they carry a credit card. The responses are listed in the table. $$\begin{array} { l | c | c | c } 
{ \text { Class } } & \begin{array} { c } 
\text { Credit Card } \
\text { Carrier }
\end{array} & \begin{array} { c } 
\text { Not a Credit Card } \
\text { Carrier }
\end{array} & \text { Total } \
\hline \text { Freshman } & 49 & 11 & 60 \
\text { Sophomore } & 12 & 28 & 40 \
\text { Total } & 61 & 39 & 100
\end{array}$$ If a student is selected at random, find the probability that he or she is a freshman given that the student owns a credit card. Round your answers to three decimal places.

Accepted Answer

The probability that a student is a freshman given that the student owns a credit card is:P(Freshman | Credit Card Carrier) = P(Freshman and Credit Card Carrier) / P(Credit Card Carrier)= 49 / 61= 0.803 (rounded to three decimal places)

Question 15

Provide an appropriate response.
-Classify the events as dependent or independent. Events A and B where P(A)= 0.8, P(B)= 0.8, and P(A and B)= 0.63

Accepted Answer

If two events A and B are independent, then P(A and B)=P(A) x P(B). However, in this case, P(A) x P(B)= 0.8 x 0.8= 0.64, which is not equal to P(A and B)=0.63. Therefore, the events are dependent. If events A and B were independent, the probability of both events occurring together would be P(A)*P(B) = 0.8*0.8 = 0.64 which is greater than P(A and B) = 0.63. Therefore, events A and B are dependent.

Question 16

Provide an appropriate response.
-A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a heart.

Accepted Answer

There are 13 hearts in a deck of 52 cards, so there are 39 cards that are not hearts. The odds in favor of picking a card that is not a heart are 39 to 13, which simplifies to 3:1.

Question 17

Provide an appropriate response.
-At the local racetrack, the favorite in a race has odds 3:2 of winning. What is the probability that the favorite wins the race?

Accepted Answer

To find the probability, we need to divide the number of ways the favorite can win by the total number of possible outcomes. The odds of 3:2 mean that for every 5 races, the favorite wins 3 times and loses 2 times. So, the probability of winning is 3/5 or 0.6. Therefore, the best choice is A. The probability of an event happening is calculated by dividing the number of favorable outcomes by the number of possible outcomes. In this case, the odds are given as 3:2, which means that for every 3 favorable outcomes (winning), there are 2 unfavorable outcomes (losing). Therefore, the probability of winning is 3/(3+2) = 0.6 or 60%.

Question 18

Provide an appropriate response.
-The $\mathrm { P } ( \mathrm { A } ) = \frac { 3 } { 5 }$ Find the odds of winning an A.

Accepted Answer

The odds of winning an A are calculated as the ratio of the probability of winning to the probability of losing. Given $\mathrm { P } ( \mathrm { A } ) = \frac { 3 } { 5 }$, the probability of losing is $1 - \frac { 3 } { 5 } = \frac { 2 } { 5 }$. Therefore, the odds of winning are $3:2$.

Question 19

Provide an appropriate response.
-A group of students were asked if they carry a credit card. The responses are listed in the table. $$\begin{array} { l | c | c | c } 
{ \text { Class } } & \begin{array} { c } 
\text { Credit Card } \
\text { Carrier }
\end{array} & \begin{array} { c } 
\text { Not a Credit Card } \
\text { Carrier }
\end{array} & \text { Total } \
\hline \text { Freshman } & 21 & 39 & 60 \
\text { Sophomore } & 18 & 22 & 40 \
\text { Total } & 39 & 61 & 100
\end{array}$$ If a student is selected at random, find the probability that he or she is a sophomore given that the student owns a credit card. Round your answers to three decimal places.

Accepted Answer

The probability that a student is a sophomore given that the student owns a credit card is calculated using conditional probability: P(Sophomore | Credit Card) = P(Sophomore and Credit Card) / P(Credit Card) = 18/39 = 0.462.

Question 20

Provide an appropriate response.
-Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that it will rain tomorrow is 63%.

Accepted Answer

The statement reflects someone's personal belief or opinion about the chance of rain, making it a subjective probability. Since the statement is based on personal belief or judgement, it falls under the category of subjective probability.

Quiz 3: Probability

Provide an appropriate response. -Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is Replaced before the second card is drawn.

Provide an appropriate response. -Classify the events as dependent or independent. Events A and B where P(A) = 0.8, P(B) = 0.2, and P(A and B) = 0.16

Provide an appropriate response. -At the local racetrack, the favorite in a race has odds 3:2 of losing. What is the probability that the favorite wins the race?

Write the word or phrase that best completes each statement or answers the question -Explain why the following statement is incorrect: He gave 110% effort.

Provide an appropriate response. -Classify the events as dependent or independent. Event A: A red candy is selected from a package with 30 colored candies and eaten. Event B: A blue candy is selected from the same package and eaten.

Provide an appropriate response. -Classify the events as dependent or independent. The events of getting two aces when two cards are drawn from a deck of playing cards and the first card is not replaced before the second card is drawn.

Write the word or phrase that best completes each statement or answers the question. -Find the probability of answering two true or false questions correctly if random guesses are made. Only one of the choices is correct.

Provide an appropriate response. -Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a newborn baby is a boy iis $\frac { 1 } { 2 }$

Provide an appropriate response. -Classify the events as dependent or independent. Events A and B where P(A) = 0.8, P(B) = 0.8, and P(A and B) = 0.63

Provide an appropriate response. -A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a heart.

Provide an appropriate response. -At the local racetrack, the favorite in a race has odds 3:2 of winning. What is the probability that the favorite wins the race?

Provide an appropriate response. -The $\mathrm { P } ( \mathrm { A } ) = \frac { 3 } { 5 }$ Find the odds of winning an A.

Provide an appropriate response. -Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that it will rain tomorrow is 63%.