Understanding Archery Risks: RSI & Eye Strain

[ivan_x3000]

Homework Statement

Each year, 5.7% of archers develop repetitive strain injury (RSI) in their arm.
Each year, 3.6% of archers develop problems related to eye strain.
However, 91.2% of archers develop neither.
(a) Formally define sensible event notation, and summarise the information in the question.
(b) List the elements in the sample space using formal notation.
(c) What is the probability that an archer develops both RSI and eye strain in a particular year?
(d) With regard to archers, are the two problems of developing RSI and developing eye strain statistically independent? Briefly explain why or why not.

Homework Equations

Have to choose between bernoulli, binomial, poisson, geometric, hyper geometric and negative binomial methods

The Attempt at a Solution

a) let P(a) = 5.7%, P(b)=3.5%, P(c)=91.2%
P(A∪B∪C)=1
b)S{P(a), P(b), P(c)}

c) 1-0.912 = 0.088

d) They are statistically independent since they affect separate parts of the body and the problems caused do not necessarily have an effect on the development of either ailments.

Also am i posting on the wrong thread none were assigned to statistics

 

[HallsofIvy]

Homework Statement

Each year, 5.7% of archers develop repetitive strain injury (RSI) in their arm.
Each year, 3.6% of archers develop problems related to eye strain.
However, 91.2% of archers develop neither.
(a) Formally define sensible event notation, and summarise the information in the question.
(b) List the elements in the sample space using formal notation.
(c) What is the probability that an archer develops both RSI and eye strain in a particular year?
(d) With regard to archers, are the two problems of developing RSI and developing eye strain statistically independent? Briefly explain why or why not.

Homework Equations

Have to choose between bernoulli, binomial, poisson, geometric, hyper geometric and negative binomial methods

No, you don't. There is no part of the problem that requires a specific probability distribution.

The Attempt at a Solution

a) let P(a) = 5.7%, P(b)=3.5%, P(c)=91.2%
P(A∪B∪C)=1
b)S{P(a), P(b), P(c)}

None of this is "sensible" until you have said what "a", "b", and "c" represent! Are "A", "B", and "C" supposed to be the same as "a", "b", and "c"? It is not a good idea to mix capital letters and small letters.

c) 1-0.912 = 0.088

NO! 0.912 was given as "the probability that archers develop neither". 1- 0.912 would be the probability they develop either or both, NOT the probability they develop both only.

d) They are statistically independent since they affect separate parts of the body and the problems caused do not necessarily have an effect on the development of either ailments.

This was not a question about physiology! What about the numbers given tell you that the are, or are not, independent?

Also am i posting on the wrong thread none were assigned to statistics

 

[ivan_x3000]

a) Let a=RSI, b=eye strain, a'c'=a^c*a^c=neither
P(a)=0.057, P(b)=0.036, P(a'b')=0.912

b) S[0.57, 0.036, 0.912]

c) (0.057)*(0.036)=0.002052

d) The values are statistically independent, in oder to to be statistically dependent at least one of the outcomes must have an effect on the other this is not the case for the set.

 

[ivan_x3000]

No, you don't. There is no part of the problem that requires a specific probability distribution.


None of this is "sensible" until you have said what "a", "b", and "c" represent! Are "A", "B", and "C" supposed to be the same as "a", "b", and "c"? It is not a good idea to mix capital letters and small letters.


NO! 0.912 was given as "the probability that archers develop neither". 1- 0.912 would be the probability they develop either or both, NOT the probability they develop both only.


This was not a question about physiology! What about the numbers given tell you that the are, or are not, independent?

how about now?

 

[Ray Vickson]

a) Let a=RSI, b=eye strain, a'c'=a^c*a^c=neither
P(a)=0.057, P(b)=0.036, P(a'b')=0.912

b) S[0.57, 0.036, 0.912]

c) (0.057)*(0.036)=0.002052

d) The values are statistically independent, in oder to to be statistically dependent at least one of the outcomes must have an effect on the other this is not the case for the set.

Your [0.57, 0.036, 0.912] does not answer question (b). You are giving a list of numbers, not a list of events. Your answer to (c) is assuming independence; you cannot do that, because the whole point of question (d) is to test whether or not this assumption is supported by the data.

Hint: look up "inclusion-exclusion principle".

 

[ivan_x3000]

Your [0.57, 0.036, 0.912] does not answer question
Hint: look up "inclusion-exclusion principle".

How about S={0.57, 0.036, 0.912}