Probability/Odds story problem

[TheBac]

I hate theoretical math. I want to calculate the probability/odds of something happening and dont know how to do it. Hoping someone here has some background in this dept.



We've had 2 backing accidents in our center in 2011. Using rough averages, our center puts 43 drivers on the street every day, and we have averaged 1100 total backing instances every day. 30 weeks have elapsed in 2011.


1) What are the odds that a backing accident will occur in general per day/week?
2) What are the odds that one driver out of the 43 will have a backing accident per day/week -- based on the total backs during the day/weeks?

I hope Im wording that right for what Im looking for. Im looking for "1 in xxxxx" type answers for both questions. Thanks ahead of time for any help.

 

[blk smoke lb7]

So 43 drivers back up and average of 1100 times per day correct?

 

[blk smoke lb7]

well 5 working days in a week so 5X 30 is 180 days work days that is so i would say the odds are 1 driver every 90 or 1 every 15 weeks rite?

 

[TheBac]

So 43 drivers back up and average of 1100 times per day correct?

Yes.

 

[blk smoke lb7]

you have 1 accident every 90days there will be 1 backing accident every 99,000 backings for your 43 drivers not quite sure how to convert this to % of accidents perday as a rough answer if you had 1 accident every 100 days that would be 1% per day divided by 43 which is 0.023255814% so rounding up.03% roughly


Wow how did i pull that out of my a$$ hope its rite Tom

 

[Osubeaver]

First off, I believe you can ignore the number of backings per week, as it is a constant.


Assume a 250 day work year.

30 weeks X 5 days = 150 company days

43 workers x 150 days = 6450 man days
<O</O
2 accidents in 150 company days = you will have an accident once out of every 75 company days.<O</O

2 accidents in 6450 man days = 1 accident every for every worker every 3225 man days (6450/2)
<O</O
3225 man days = 12.9 years …in other words you could say a single driver will back into something once every 12.9 years<O</O

You could also say 2 accidents for 43 drivers in 150 days could extrapolate to 3.33 accidents per year (250 work days/150 days so far x 2 accidents). So 3.33 out of 43….or 1 in 12.912. (3.33/43)=(1/x) -> 3.333x = 43 -> x = 43/3.33 = 12.912 <O</O


2 accidents in 30 weeks = 1 every 15 weeks, or 1/15th of an accident per week......so 1 in 15 weeks or 1 in 75 chance per day company wide.

or 2 accidents per 43 drivers in 150 days.........2/(43 x 150days) = 1/x....2/6450 = 1/x....... 1 in 3225 chance per day per driver

I caught a couple of transposed numbers in there....I think they're fixed but somebody check that math. A bunch of ways to say the same thing anyway.

 

[blk smoke lb7]

Sorry Tom guess i screwed that 1 up

 

[ripmf666]

If we go by what Gm tells us it will not happen we can stop it from happening to begin with lol.

 

[McRat]

DOH! Read the problem wrong. Will respond later.

 

[TheBac]

First off, I believe you can ignore the number of backings per week, as it is a constant.


Assume a 250 day work year.

30 weeks X 5 days = 150 company days

43 workers x 150 days = 6450 man days
<O</O
2 accidents in 150 company days = you will have an accident once out of every 75 company days.<O</O

2 accidents in 6450 man days = 1 accident every for every worker every 3225 man days (6450/2)
<O</O
3225 man days = 12.9 years …in other words you could say a single driver will back into something once every 12.9 years<O</O

You could also say 2 accidents for 43 drivers in 150 days could extrapolate to 3.33 accidents per year (250 work days/150 days so far x 2 accidents). So 3.33 out of 43….or 1 in 12.912. (3.33/43)=(1/x) -> 3.333x = 43 -> x = 43/3.33 = 12.912 <O</O


2 accidents in 30 weeks = 1 every 15 weeks, or 1/15th of an accident per week......so 1 in 15 weeks or 1 in 75 chance per day company wide.

or 2 accidents per 43 drivers in 150 days.........2/(43 x 150days) = 1/x....2/6450 = 1/x....... 1 in 3225 chance per day per driver

I caught a couple of transposed numbers in there....I think they're fixed but somebody check that math. A bunch of ways to say the same thing anyway.

Wow. Thanks Jerry! I guess I am a "typical" driver, because I've had 2 backing accidents in 26 years. Wish they didnt happen, but they did.

 

[skintback]

Shit happens that's not bad for 26 years :thumb: