Benjamin Odei F2021STAT213
Assignment 2 is due on Monday, October 18, 2021 at 11:59pm.
The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you
should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help.
There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s
not very efficient or effective.
Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e ∧ (ln(2)) instead of 2, (2 +
tan(3)) ∗ (4 − sin(5)) ∧ 6 − 7/8 instead of 27620.3413, etc.
Problem 1. (1 point) Problem 2. (1 point)
The Canadian Tobacco Monitoring Survey is a national survey An instructor gives his class a set of 16 problems with the infor-
administered by Statistics Canada to study smoking trends of mation that the next quiz will consist of a random selection of 4
Canadians aged 15 or older. The most recent survey found that of them. If a student has figured out how to do 7 of the problems,
19.45% of Canadians aged 15 years or older smoke on a daily what is the probability the he or she will answer correctly
basis. In addition, 22% of men are smokers, and 17% of women
are smokers. (a) all 4 problems?
The most recent census shows that men make up 49% of the (b) at least 3 problems?
Canadian population, with women making up the remainder.
Answer(s) submitted:
You randomly pick a Canadian that is 15 years old or older. •
Compute the probability this person •
(incorrect)
Part (a) is male and a smoker. (Use four decimals in
your answer)
Part (b) is a women and not a smoker. (Use four decimals)
Part (c) What percentage of smokers are male? %(enter
your percentage to two decimals)
Problem 3. (1 point)
Part (d) What percentage of smokers are women? % % (en-
ter your percentage to two decimals) Let A and B be two events where P(A) = 0.5, P(B) = 0.22, and
Answer(s) submitted: P(Bc |Ac ) = 0.89. What is the probability of A or B?
•
• (Use four decimals in your answer)
•
•
(incorrect) Answer(s) submitted:
•
(incorrect)
1
, Problem 4. (1 point) Problem 6. (1 point)
You ask your roommate to mail a letter for you. Suppose there is A Statistics professor takes two hockey sticks - Brand A and
a 0.2 probability your roommate will forget to mail it. Brand B - to each game he plays. Since Brand A is a newer stick
than Brand B, so he believes the chance he will break his Brand
Should your roommate mail your letter, there is a 0.92 proba- A stick in a game is 9%; he also believes the probability he will
bility that Canada Post will deliver the letter. break Brand B in a game is 0.12.
Due to his various superstitions, he is 2-times more likely to
If the letter is never delivered, what is the probability that your use his Brand A hockey stick to start a game than the Brand B
roommate mailed the letter? (Use four decimals in your stick.
answer)
Part (a) Find the probability that he will use his Brand A hockey
stick at the start of a hockey game. (use four decimals in
your answer)
Not sure how to perform some of the tasks? Click to see similar problem
Answer(s) submitted:
• Part (b) Keeping in mind that he could use either Brand A or
(incorrect) Brand B to start the game, what is the probability that the stick he
uses at the start of the game breaks? (use four decimals)
Problem 5. (1 point) Part (c) If he breaks the stick he started the game with, what is
A Canadian male has recently had a Prostate Specific Antigen the probability that he started the game with Brand B? (use
(PSA) test as to determine if he has prostate cancer. The false- four decimals)
positive rate of a PSA test is 16%. If he does have prostate cancer, Answer(s) submitted:
PSA test will be positive 81% of the time. •
•
•
Because this male is showing symptoms that are consistent with
prostate cancer, it is assumed that the chance he has prostate (incorrect)
cancer prior to taking the PSA test is 0.16.
Part (a) What is the probability that the PSA test will yield a
positive result?
(use four decimals in your answer)
Part (b) If the PSA test gives a positive result, what is the proba-
bility that he does not have prostate cancer?
(use four decimals)
Part (c) Suppose the PSA test result is negative, indicating that
he does not have prostate cancer and his symptoms are a result of
something else. What is the probability that he does have prostate
cancer?
(use four decimals)
Answer(s) submitted:
•
•
•
(incorrect)
2
Assignment 2 is due on Monday, October 18, 2021 at 11:59pm.
The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error, you
should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help.
There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s
not very efficient or effective.
Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e ∧ (ln(2)) instead of 2, (2 +
tan(3)) ∗ (4 − sin(5)) ∧ 6 − 7/8 instead of 27620.3413, etc.
Problem 1. (1 point) Problem 2. (1 point)
The Canadian Tobacco Monitoring Survey is a national survey An instructor gives his class a set of 16 problems with the infor-
administered by Statistics Canada to study smoking trends of mation that the next quiz will consist of a random selection of 4
Canadians aged 15 or older. The most recent survey found that of them. If a student has figured out how to do 7 of the problems,
19.45% of Canadians aged 15 years or older smoke on a daily what is the probability the he or she will answer correctly
basis. In addition, 22% of men are smokers, and 17% of women
are smokers. (a) all 4 problems?
The most recent census shows that men make up 49% of the (b) at least 3 problems?
Canadian population, with women making up the remainder.
Answer(s) submitted:
You randomly pick a Canadian that is 15 years old or older. •
Compute the probability this person •
(incorrect)
Part (a) is male and a smoker. (Use four decimals in
your answer)
Part (b) is a women and not a smoker. (Use four decimals)
Part (c) What percentage of smokers are male? %(enter
your percentage to two decimals)
Problem 3. (1 point)
Part (d) What percentage of smokers are women? % % (en-
ter your percentage to two decimals) Let A and B be two events where P(A) = 0.5, P(B) = 0.22, and
Answer(s) submitted: P(Bc |Ac ) = 0.89. What is the probability of A or B?
•
• (Use four decimals in your answer)
•
•
(incorrect) Answer(s) submitted:
•
(incorrect)
1
, Problem 4. (1 point) Problem 6. (1 point)
You ask your roommate to mail a letter for you. Suppose there is A Statistics professor takes two hockey sticks - Brand A and
a 0.2 probability your roommate will forget to mail it. Brand B - to each game he plays. Since Brand A is a newer stick
than Brand B, so he believes the chance he will break his Brand
Should your roommate mail your letter, there is a 0.92 proba- A stick in a game is 9%; he also believes the probability he will
bility that Canada Post will deliver the letter. break Brand B in a game is 0.12.
Due to his various superstitions, he is 2-times more likely to
If the letter is never delivered, what is the probability that your use his Brand A hockey stick to start a game than the Brand B
roommate mailed the letter? (Use four decimals in your stick.
answer)
Part (a) Find the probability that he will use his Brand A hockey
stick at the start of a hockey game. (use four decimals in
your answer)
Not sure how to perform some of the tasks? Click to see similar problem
Answer(s) submitted:
• Part (b) Keeping in mind that he could use either Brand A or
(incorrect) Brand B to start the game, what is the probability that the stick he
uses at the start of the game breaks? (use four decimals)
Problem 5. (1 point) Part (c) If he breaks the stick he started the game with, what is
A Canadian male has recently had a Prostate Specific Antigen the probability that he started the game with Brand B? (use
(PSA) test as to determine if he has prostate cancer. The false- four decimals)
positive rate of a PSA test is 16%. If he does have prostate cancer, Answer(s) submitted:
PSA test will be positive 81% of the time. •
•
•
Because this male is showing symptoms that are consistent with
prostate cancer, it is assumed that the chance he has prostate (incorrect)
cancer prior to taking the PSA test is 0.16.
Part (a) What is the probability that the PSA test will yield a
positive result?
(use four decimals in your answer)
Part (b) If the PSA test gives a positive result, what is the proba-
bility that he does not have prostate cancer?
(use four decimals)
Part (c) Suppose the PSA test result is negative, indicating that
he does not have prostate cancer and his symptoms are a result of
something else. What is the probability that he does have prostate
cancer?
(use four decimals)
Answer(s) submitted:
•
•
•
(incorrect)
2
