List of Questions for Probability and Permutation

[noviceprobability]

Hello , sorry I have a quiz coming soon and I am rushing to understand these questions but I cannot understand. I hope someone can help me in these! Its a long list for several questions but the answers are provided.. I need the workings and explanations though. I am afraid of failing my quiz.

Question 3
Find the number of different signals that can be generated by arranging exactly 2 flags in order (one below the other) on a vertical staff, if five different flags are available.



The answer provided was '' The order of the flags determines the meaning of the signal so in this case we calculate the number of permutations of 2 to 5 .

So what is the numerical answer for this question? I do not understand because is this question supposed to be repetition of flags allowed or no repetition?


Question 6
0 out of 10 points
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

a) The likelihood that a student lists music as a hobby
Correct Answer:
Correct 0.6
Answer range +/-
0 (0.6 - 0.6)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
P(M) = 0.6 is an example of simple probability

Is the working 60 divided by 100 to give you 0.6?




Question 7
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

b) The probability that a student participates in music, sport and socialising,
Correct Answer:
Correct 0.204
Answer range +/-
0 (0.204 - 0.204)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
The events are independent so P(M and Sp and Sc) = 0.205 is an example of joint probability calculated using the multiplication rule

I do not know how to get answer 0.205 because there is no workings.

Question 8
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:
c) The probability that a student lists music or sport as a hobby.
Correct Answer:
Correct 0.76
Answer range +/-
0 (0.76 - 0.76)
Response Feedback:
Use the general addition rule

What is the maths working for this? I do not know because there is no workings provided , only answers and I do not know how to find the answers.

Question 9
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:
a) P(C | F);
Correct Answer:
Correct 0.06
Answer range +/-
0 (0.06 - 0.06)

Is P(C | F) = P(C&F) divided by P(F) ? Or is P(C | F) = P(C) divided by P(F)? I am getting confused.

Question 10
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

b) P(C and F);
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

Likewise , it seems the questions are interrelated so I can't do the rest without solving the previous questions I guess. And I am confused by P(C&F). Is P(C&F) = P(C) divided by P(F)? or is P(C&F) equals P(C)+P(F)?


Question 11
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

c) P(F | C);
Correct Answer:
Correct 0.5
Answer range +/-
0 (0.5 - 0.5)

Workings needed.

Question 12
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

d) P(C and M), where M is the event that a student is male;
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

i tried P(C) divided by P(M) and it was 0.03 divided by 0.5 and it gave me a different answer to the correct answer. I am lost .

 

[Deleted member 4993]

Hello , sorry I have a quiz coming soon and I am rushing to understand these questions but I cannot understand. I hope someone can help me in these! Its a long list for several questions but the answers are provided.. I need the workings and explanations though. I am afraid of failing my quiz.

Question 3
Find the number of different signals that can be generated by arranging exactly 2 flags in order (one below the other) on a vertical staff, if five different flags are available.



The answer provided was '' The order of the flags determines the meaning of the signal so in this case we calculate the number of permutations of 2 to 5 .

Since you do not understand permutation - you can count the pairs!!

How many ways can you fly 2 flags on a pole?

Lets name those flags - a, b, c, d & e

We can choose:

ab, ba, ac , ca, ad, da, ae, ea ..... and

bc, cb, bd, db, be, eb ...... and

cd, dc, ce, ec ..... and

de, ed

How many are those....

So what is the numerical answer for this question? I do not understand because is this question supposed to be repetition of flags allowed or no repetition?


Question 6
0 out of 10 points
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

a) The likelihood that a student lists music as a hobby
Correct Answer:
Correct 0.6
Answer range +/-
0 (0.6 - 0.6)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
P(M) = 0.6 is an example of simple probability

Is the working 60 divided by 100 to give you 0.6?




Question 7
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

b) The probability that a student participates in music, sport and socialising,
Correct Answer:
Correct 0.204
Answer range +/-
0 (0.204 - 0.204)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
The events are independent so P(M and Sp and Sc) = 0.205 is an example of joint probability calculated using the multiplication rule

I do not know how to get answer 0.205 because there is no workings.

Question 8
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:
c) The probability that a student lists music or sport as a hobby.
Correct Answer:
Correct 0.76
Answer range +/-
0 (0.76 - 0.76)
Response Feedback:
Use the general addition rule

What is the maths working for this? I do not know because there is no workings provided , only answers and I do not know how to find the answers.

Question 9
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:
a) P(C | F);
Correct Answer:
Correct 0.06
Answer range +/-
0 (0.06 - 0.06)

Is P(C | F) = P(C&F) divided by P(F) ? Or is P(C | F) = P(C) divided by P(F)? I am getting confused.

Question 10
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

b) P(C and F);
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

Likewise , it seems the questions are interrelated so I can't do the rest without solving the previous questions I guess. And I am confused by P(C&F). Is P(C&F) = P(C) divided by P(F)? or is P(C&F) equals P(C)+P(F)?


Question 11
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

c) P(F | C);
Correct Answer:
Correct 0.5
Answer range +/-
0 (0.5 - 0.5)

Workings needed.

Question 12
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

d) P(C and M), where M is the event that a student is male;
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

i tried P(C) divided by P(M) and it was 0.03 divided by 0.5 and it gave me a different answer to the correct answer. I am lost .

.

 

[Steven G]

Hello , sorry I have a quiz coming soon and I am rushing to understand these questions but I cannot understand. I hope someone can help me in these! Its a long list for several questions but the answers are provided.. I need the workings and explanations though. I am afraid of failing my quiz.

Question 3
Find the number of different signals that can be generated by arranging exactly 2 flags in order (one below the other) on a vertical staff, if five different flags are available.



The answer provided was '' The order of the flags determines the meaning of the signal so in this case we calculate the number of permutations of 2 to 5 .

So what is the numerical answer for this question? I do not understand because is this question supposed to be repetition of flags allowed or no repetition? If only 5 flags are available and they are different then how can you have repetition?


Question 6
0 out of 10 points
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

a) The likelihood that a student lists music as a hobby
Correct Answer:
Correct 0.6
Answer range +/-
0 (0.6 - 0.6)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
P(M) = 0.6 is an example of simple probability

Is the working 60 divided by 100 to give you 0.6?



Question 7
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:

b) The probability that a student participates in music, sport and socialising,
Correct Answer:
Correct 0.204
Answer range +/-
0 (0.204 - 0.204)
Response Feedback:
Let M be the event that a student likes Music, Let Sp be the event that a student likes Sport, Let Sc be the event that a student likes Socialising
The events are independent so P(M and Sp and Sc) = 0.205 is an example of joint probability calculated using the multiplication rule

I do not know how to get answer 0.205 because there is no workings.

Question 8
In a random sample of 100 students 60 list music as one of their hobbies, 40 list sport as a hobby and 85 list socialising as a hobby. Assume the events are statistically independent. Use Venn diagrams to calculate the following:
c) The probability that a student lists music or sport as a hobby.
Correct Answer:
Correct 0.76
Answer range +/-
0 (0.76 - 0.76)
Response Feedback:
Use the general addition rule

What is the maths working for this? I do not know because there is no workings provided , only answers and I do not know how to find the answers.

Question 9
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:
a) P(C | F);
Correct Answer:
Correct 0.06
Answer range +/-
0 (0.06 - 0.06)

Is P(C | F) = P(C&F) divided by P(F) ? Or is P(C | F) = P(C) divided by P(F)? I am getting confused.

Question 10
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

b) P(C and F);
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

Likewise , it seems the questions are interrelated so I can't do the rest without solving the previous questions I guess. And I am confused by P(C&F). Is P(C&F) = P(C) divided by P(F)? or is P(C&F) equals P(C)+P(F)?


Question 11
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

c) P(F | C);
Correct Answer:
Correct 0.5
Answer range +/-
0 (0.5 - 0.5)

Workings needed.

Question 12
0 out of 10 points
At a certain university function, 6% of the participants are commerce students, event C. 50% of all participants are female, event F while 3% of participants are females and commerce students. Suppose a participant is selected at random. Use a contingency table to help find the following probabilities and interpret the result:

d) P(C and M), where M is the event that a student is male;
Correct Answer:
Correct 0.03
Answer range +/-
0 (0.03 - 0.03)

i tried P(C) divided by P(M) and it was 0.03 divided by 0.5 and it gave me a different answer to the correct answer. I am lost .

See red above

 

[Ishuda]

...
Question 3
...
So what is the numerical answer for this question? I do not understand because is this question supposed to be repetition of flags allowed or no repetition?

Study the question a little closer and see what is true but not said about the problem. For example, you ask 'is repetition allowed'. If you use a flag for a particular position in a signal, can you re-use it in the same signal. Not the way the problem is stated, i.e. 'by arranging exactly 2 flags in order'.

Question 6
...
Is the working 60 divided by 100 to give you 0.6?

Yes

Question 7
,,,
I do not know how to get answer 0.205 because there is no workings.

You are given the formula for independent events, so what is P(music)*P(sports)*P(socializing)

Question 8
...
What is the maths working for this? I do not know because there is no workings provided , only answers and I do not know how to find the answers.

As with your other questions, you are going to have to learn the proper formulas [or deduce in a short while if you are taking a test]. In this case, you have
P(A or B) = P(A) + P(B) - what you have already counted
What you have already counted is the overlap, i.e. P(A and B).

Question 9
...
Is P(C | F) = P(C&F) divided by P(F) ? Or is P(C | F) = P(C) divided by P(F)? I am getting confused.

Again, study and understand the rule: P(C|F) means we are restricting our population size to p_o*P(F) where p_o is the original population size. It also means the both C and F must occur. So the population for both C and F is p_o*P(C and F).

Question 10
...
Likewise , it seems the questions are interrelated so I can't do the rest without solving the previous questions I guess. And I am confused by P(C&F). Is P(C&F) = P(C) divided by P(F)? or is P(C&F) equals P(C)+P(F)?

As in (3), make sure you read the question, i.e. '3% of participants are females and commerce students'

Question 11
...
Workings needed.

Look at (9) except, since the events are not independent, you need to be given P(C and F) [for which see 10]

Question 12
...
i tried P(C) divided by P(M) and it was 0.03 divided by 0.5 and it gave me a different answer to the correct answer. I am lost .

Well, first of all we need to assume something about the population and that is 'if you are not female, your are male'. Thus P(M) would be 0.5. Again, learn the equations or how to deduce them [and quickly if in a test]: If P(C)=.06 and P(C and F)=.03, what does that suggest about P(C and (not F))=P(C and M)? What formula does that suggest?