SOLUTION: At certain times of the year, about 70% of airline flight delays are caused by bad weather. During those times, about 50% of all flights experience bad weather, and about 25% of

Algebra ->  Probability-and-statistics -> SOLUTION: At certain times of the year, about 70% of airline flight delays are caused by bad weather. During those times, about 50% of all flights experience bad weather, and about 25% of       Log On


   

Question 894108:
At certain times of the year, about 70% of airline flight delays are caused by bad weather. During those times, about 50% of all flights experience bad weather, and about 25% of all flights are delayed.
Given these percentages, if the weather is good, what is the probability that your flight will be delayed?
About 15%
About 20%
About 35%
About 30%
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this depends a lot on interpretation.
my interpretation follows.
25% of all flights are delayed.
70% of those are delayed by bad weather.
the rest are delayed for not having to do with bad weather which could occur in bad weather or good weather.
if i assume a total of 1000 flights, then 25% of 1000 = 250 flights will be delayed for some reason or other.
70% of those will be delayed because of bad weather.
this means that .7 * 250 = 175 flights will be delayed because of bad weather and 75 flights will be delayed due to causes not having to do with bad weather.
so you have, out of a total of 1000 flights, 175 are delayed due to bad weather and 75 are delayed for causes other than bad weather.

now we'll see if we can figure out what the percentages should be.

the question is:

if the weather is good, what is the percentage of time that your flight will be delayed.

since the weather is good, this means that 500 flights are affected because 50% of the flights experience good weather and 50% of the flights experience bad weather.

there will be 75 flights that are delayed due to causes other than bad weather

if you assume that all of the flights that are not caused by bad weather occur in good weather, then the probability would have to be 75 / 500 = .15 = 15%.

i suspect that's your answer.

it doesn't take into account that the plane could be delayed due to causes other than bad weather even if the weather is bad.

unfortunately, if you take that into account, the percentage becomes 7.5% and that is not one of your options, so i would go with 15% under the assumption that cause other than due to bad weather occur only in good weather.

that's my interpretation.
since this is a difficult problem to interpret, it's my best guess.