The Question
"Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 15% of flights are late because of weather and ground operations. What is the probability that a flight arrives late because of weather or ground operations? (2 numbers behind decimal, example: 0.34)"
The Supposed Solution
My friend just did this: $0.75+0.35-0.15=0.95$
My Question
This may be an overcomplication, but I just feel that there is something wrong with this question. How is it possible for a portion, represented by percentages, to total larger than 100%? Is it just me or is the question mistaken?
Best Answer
There are no errors in the question. Look at this Venn representation of your problem
where the red circle is the event: late due to weather conditions and the blue one is the event: late for Ground operations
What is the probability that an airplane arrives late ONLY for weather conditions? Obviously it is not 75% because this probability does not exclude to have both bad weather conditions AND ground operations too...