Question 1

A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find theprobability of getting the same outcome on each toss.

Accepted Answer

The answer of A fair coin is tossed two times...

Question 2

This problem deals with eye color, an inherited trait. For purposes of this problem, assume that only two eyecolors are possible, brown and blue. We use b to represent a blue eye gene and B a brown eye gene. If any Bgenes are present, the person will have brown eyes. The table shows the four possibilities for the children oftwo Bb (brown-eyed) parents, where each parent has one of each eye color gene. $\begin{array}{cc|cc} 
&&\text { Second Parent } \
& & \mathrm{B} & \mathrm{b} \
\hline & \mathrm{B} & \mathrm{BB} & \mathrm{Bb} \
 \text { First Parent }  \
& \mathrm{b} & \mathrm{Bb} & \mathrm{bb}
\end{array}$

Find the probability that these parents give birth to a child who has blue eyes.

Accepted Answer

The table shows that out of the four possible gene combinations (BB, Bb, Bb, bb), only one combination (bb) results in blue eyes. Therefore, the probability is $\frac{1}{4}$.

Question 3

A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.

Accepted Answer

Since a die only has sides numbered 1 through 6, it is impossible to roll a 10, making the probability of such an event 0.

Question 4

The ______________ probability of an outcome is obtained by dividing the frequency of occurrence of an eventby the number of trials of the experiment.

Accepted Answer

Empirical probability is calculated by dividing the number of times an event occurs by the total number of trials or observations. This approach is based on actual results from experiments or observations, rather than theoretical calculations or personal beliefs.

Question 5

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that cab fares will rise during the winter is 0.05.

Accepted Answer

This is a subjective probability because it is based on personal judgment or opinion rather than on exact calculations or specific past events.

Question 6

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. We watched a friend play roulette for two hours. In that time we noted that the wheel was spun 50 times and that out of those 50 spins black came up 22 times. Based on this data, the $\mathrm { P } ( \mathrm { black } ) = \frac { 22 } { 50 } = 0.44$. This is an example of what type of probability?

Accepted Answer

Empirical probability is calculated based on the outcomes of an experiment or past data, which is exactly what is described in the scenario where the probability of landing on black is determined by observing 50 spins of the roulette wheel.

Question 7

A single die is rolled twice. The set of 36 equally likely outcomes is  {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1) ,  (2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1) ,  (5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} . Find the probability of getting two numbers whose sum is greater than 9 and less than  13 .

Accepted Answer

The answer of A single die is rolled twice. The...

Question 8

Classify the statement as an example of classical probability, empirical probability, or subjective probability.In one state lottery, a person selects a 4-digit number. The probability of winning this stateʹs lottery is 10,0001 .

Accepted Answer

Classical probability is used when all outcomes are equally likely. Since there are 10,000 possible 4-digit combinations (0000 to 9999) and each combination has an equal chance of being drawn, calculating the probability of winning by selecting one specific combination fits the definition of classical probability.

Question 9

Three fair coins are tossed in the air and land on a table. The up side of each coin is noted. How manyelements are there in the sample space?

Accepted Answer

Each coin has 2 possible outcomes (heads or tails), and since there are 3 coins, the total number of outcomes in the sample space is 2^3 = 8.

Question 10

The ______________ probability of an outcome is obtained by dividing the number of ways an event can occurby the number of possible outcomes.

Accepted Answer

Classical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, assuming each outcome is equally likely.

Question 11

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The $\mathrm { P } ($ Red $) = \frac { 18 } { 20 } \approx 0.47$. This is an example of what type of probability?

Accepted Answer

Classical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is exactly what is done here with the calculation for the probability of landing on red in roulette.

Question 12

The sample space for tossing three fair coins is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. What is theprobability of exactly two heads?

Accepted Answer

The outcomes with exactly two heads are HHT, HTH, and THH, which are 3 out of the 8 total outcomes, making the probability $\frac{3}{8}$.

Question 13

A probability experiment is conducted in which the sample space of the experiment is  S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} .  Let event  A={2,3,4,5}  and event  B={12,13,14} .  Assume that each outcome is equally likely. List the outcomes in A  and  B . Are A and  B  mutually exclusive?

Accepted Answer

The answer of A probability experiment is conducted in which...

Question 14

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that it will snow tomorrow is 53%.

Accepted Answer

This is a subjective probability because it is based on personal judgment or estimation rather than on a classical or empirical method of calculation.

Question 15

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that a newborn kitten is a male $\text { is } \frac { 1 } { 2 } \text {. }$

Accepted Answer

Classical probability is used when all outcomes are equally likely, such as flipping a coin or, in this case, the 50/50 chance of a newborn kitten being male or female.

Question 16

A single die is rolled twice. The set of 36 equally likely outcomes is $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 2,1 )$, $( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,1 )$, $( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,1 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) )$. Find the probability of getting two numbers whose sum is less than 13 .

Accepted Answer

Since the maximum sum achievable with two dice is 12 (6+6), all possible outcomes (36 in total) result in sums less than 13.

Question 17

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

Accepted Answer

In a standard 52-card deck, there are 12 picture cards (4 Jacks, 4 Queens, and 4 Kings). Therefore, the probability of being dealt a picture card is $ \frac { 12 } { 52 } $, which simplifies to $ \frac { 3 } { 13 } $.

Question 18

A single die is rolled twice. The set of 36 equally likely outcomes is  [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1), ,
 (2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1) ,
 (5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} .  Find the probability of getting two numbers
whose sum is greater than  10 .

Accepted Answer

The outcomes where the sum of the two numbers is greater than 10 are: (5,6), (6,5), (6,6), (4,6), (6,4). There are 5 such outcomes out of 36 possible outcomes, so the probability is $\frac{5}{36}$, which simplifies to $\frac{1}{12}$.

Question 19

The ______________ probability of an outcome is a probability based on personal judgment.

Accepted Answer

Subjective probability is based on personal judgment or opinion rather than on objective data or specific calculations.

Question 20

Classify the statement as an example of classical probability, empirical probability, or subjective probability. Itis known that the probability of hitting a pothole while driving on a certain road is 1%.

Accepted Answer

Empirical probability is based on observations or experiments. The statement about hitting a pothole with a 1% probability is likely derived from data or past experiences, making it an empirical probability.

Quiz 5: Probability

A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find theprobability of getting the same outcome on each toss.

A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.

The ______________ probability of an outcome is obtained by dividing the frequency of occurrence of an eventby the number of trials of the experiment.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that cab fares will rise during the winter is 0.05.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.In one state lottery, a person selects a 4-digit number. The probability of winning this stateʹs lottery is 10,0001 .

Three fair coins are tossed in the air and land on a table. The up side of each coin is noted. How manyelements are there in the sample space?

The ______________ probability of an outcome is obtained by dividing the number of ways an event can occurby the number of possible outcomes.

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The $\mathrm { P } ($ Red $) = \frac { 18 } { 20 } \approx 0.47$ . This is an example of what type of probability?

The sample space for tossing three fair coins is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. What is theprobability of exactly two heads?

A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} . Let event A={2,3,4,5} and event B={12,13,14} . Assume that each outcome is equally likely. List the outcomes in A and B . Are A and B mutually exclusive?

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that it will snow tomorrow is 53%.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that a newborn kitten is a male $\text { is } \frac { 1 } { 2 } \text {. }$

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

The ______________ probability of an outcome is a probability based on personal judgment.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. Itis known that the probability of hitting a pothole while driving on a certain road is 1%.

Quiz 5: Probability

A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find theprobability of getting the same outcome on each toss.

A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.

The ______________ probability of an outcome is obtained by dividing the frequency of occurrence of an eventby the number of trials of the experiment.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that cab fares will rise during the winter is 0.05.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.In one state lottery, a person selects a 4-digit number. The probability of winning this stateʹs lottery is 10,0001 .

Three fair coins are tossed in the air and land on a table. The up side of each coin is noted. How manyelements are there in the sample space?

The ______________ probability of an outcome is obtained by dividing the number of ways an event can occurby the number of possible outcomes.

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The P(\mathrm { P } (P( Red ) =1820≈0.47) = \frac { 18 } { 20 } \approx 0.47) =2018​≈0.47 . This is an example of what type of probability?

The sample space for tossing three fair coins is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. What is theprobability of exactly two heads?

A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} . Let event A={2,3,4,5} and event B={12,13,14} . Assume that each outcome is equally likely. List the outcomes in A and B . Are A and B mutually exclusive?

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that it will snow tomorrow is 53%.

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that a newborn kitten is a male is 12. \text { is } \frac { 1 } { 2 } \text {. } is 21​.

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

The ______________ probability of an outcome is a probability based on personal judgment.

Classify the statement as an example of classical probability, empirical probability, or subjective probability. Itis known that the probability of hitting a pothole while driving on a certain road is 1%.

In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The $\mathrm { P } ($ Red $) = \frac { 18 } { 20 } \approx 0.47$ . This is an example of what type of probability?

Classify the statement as an example of classical probability, empirical probability, or subjective probability.The probability that a newborn kitten is a male $\text { is } \frac { 1 } { 2 } \text {. }$