Need pro statistician help to answer question

One individual has 4 teeth that are injured.

i There are 2 rare complications you can develop over time, each has a chance of 5% of developing in a lifetime

ii There is one other rare complication, the risk is 7.5% over a lifetime.

Q/ What is the percentage chance of this individual developing a complication?

Is it 7.5% x 4 = 28% chance over their life

Please explain the correct answer for this maths numpty so I can understand the field of statistics we are referring to. And thank you.

PS they have no letter box.

I suspect there is not enough information.

Is the risk per tooth, or per injury?

Is the second complication directly related to the first or independent of it?

Again, is it per tooth or related to the general injury?

ignore

42: The answer to life, the universe and everything.

jpod said:

PS they have no letter box.

Click to expand...

Is there an open window?

Is the risk per tooth, or per injury?

Is the second complication directly related to the first or independent of it?

Again, is it per tooth or related to the general injury?

There is only one injury, there are three potential complications which are independent of each other.

nst68 said:

Is there an open window?

Click to expand...

No, and their mouth is closed

well we are on the internet remember, so if it's a maths questions the answer is BODMAS. If it's a statistics question, then anything is the correct answer as 99% of all statistics are made up.

Glen's letter box is wide open fellas.

jpod said:

Glen's letter box is wide open fellas.

Click to expand...

In a surprising turn of events, I'm watching a film of the same name.

Could answer this but I'm not a pro so you're outa luck!

jpod said:

One individual has 4 teeth that are injured.

i There are 2 rare complications you can develop over time, each has a chance of 5% of developing in a lifetime

ii There is one other rare complication, the risk is 7.5% over a lifetime.

Q/ What is the percentage chance of this individual developing a complication?

Is it 7.5% x 4 = 28% chance over their life

Please explain the correct answer for this maths numpty so I can understand the field of statistics we are referring to. And thank you.

Click to expand...

this is just a simple probability question no?

if these are independent events (which you've stated in a further post) and unrelated to the number of individual teeth then the chance of at least one of these events occurring is

1 - chance of none occuring

= 1 - (.95 * .95 * .925)

= approximately 16.5 %

is this actually a homework question or a question you've posed here yourself - either way it seems a bit odd, how do you know you can assume independence for example? I suspect this answer is meaningless - I mean if you have 16 injured teeth are you saying you don't have an increased chance of a complication?

edited cos I'm half asleep... still think this question is relying on dubious assumptions

If you're looking for the probability of at least one tooth developing at least one complication it's 70% I think (0.05 + 0.05 + 0.075)x4 = 0.7

EDIT: ignore, completely wrong, see post #21

jpod said:

Is the risk per tooth, or per injury?

Is the second complication directly related to the first or independent of it?

Again, is it per tooth or related to the general injury?

There is only one injury, there are three potential complications which are independent of each other.

Click to expand...

I think you misunderstood his question. Is the risk of 5/7.5% the risk of any of the 4 teeth over a lifetime getting that complication or is it the risk of each tooth throughout the lifetime. If the injuries are independent of each other and with the risk for all four teeth rather than individual, the outcomes can be:

No complication

Just complication 1

Just Complication 2

Just Complication 3

1+2

1+3

2+3

Add up the red and green outcomes if the injuries are not mutually exclusive. Add up just the red if they are mutually exclusive. If the risk is for individual teeth, calculate the probability of one tooth and multiply the chances by 4.

Hmmm...

There are 3 possible complications, all independent, their chance of developing is 5%, 5% and 7% over the patient's lifetime

There are four teeth damaged by one injury, with those risks above.

What is the % chance the patient will suffer complications in their lifetime?

jpod said:

Is the risk per tooth, or per injury?

Is the second complication directly related to the first or independent of it?

Again, is it per tooth or related to the general injury?

There is only one injury, there are three potential complications which are independent of each other.

Click to expand...

Medicine is not as simple as random statistics (Like tossing a coin)

But, if the complications are..

a) related to the original injury and not per tooth
b) Genuinely unrelated to one another

I would have thought that the raw probability is as already stated.

1:20/lifetime for each of the first two

1:14/lifetime (about) for the third

If the conditions are really unrelated to one another, then the likelihood of developing more than one would normally be multiplicative.

(IE you would have to be very unlucky to get all three 0.05x0.05x0.075!)

However. In real life I suspect that the conditions will affect one another so the likelihood of developing two or more complications is likely to be rather greater than this. possibly up to the point of being additive (0.05+0.05+0.075!)

Basically you (Your Friend! ) has a basic 1:14 probability of having at least one complication at some point in his life, likely a smaller probability of having 2 or more but, if unlucky, possibly an even greater risk depending on how the conditions interact. assessing that risk is likely to be a bit of a guess in reality.

jpod said:

Hmmm...

There are 3 possible complications, all independent, their chance of developing is 5%, 5% and 7% over the patient's lifetime

There are four teeth damaged by one injury, with those risks above.

What is the % chance the patient will suffer complications in their lifetime?

Click to expand...

this is a question you're posing yourself - I think your assumptions are dubious

jpod said:

Hmmm...

There are 3 possible complications, all independent, their chance of developing is 5%, 5% and 7% over the patient's lifetime

There are four teeth damaged by one injury, with those risks above.

What is the % chance the patient will suffer complications in their lifetime?

Click to expand...

Is that the exact question that you're ctrl + V-ing ?

You need to define whether the risk is per tooth or per injury. Given the basic level of statistics and lack of information, i very much doubt the injury risks are dependant on each other as they would be irl.

If there is no more information you can assume it to be the risk for individual teeth throughout the lifetime and they chose to use four teeth to throw you off a little, it just requires multiplying the risk of one tooth by 4.

IRL diseased or injured teeth become more likely to develop more complications and so are the ones next to them, so the teeth risks can change massively due to there being many many more outcomes due to different combinations eg. Tooth 1 complication 3 + Tooth 3 + complication 2 and 3

D3lirious said:

If you're looking for the probability of at least one tooth developing at least one complication it's 70% I think (0.05 + 0.05 + 0.075)x4 = 0.7

Click to expand...

That is what I worked it out to be? At least a 70% chance that at least one of his teeth will develop one complication.