Question I don't understand on probablility

[flyingfreedom]

A company surveyed its 140 employees and determined that 32 commuted by car and 78 by train. Of these commuters, fifteen used both modes of transportation. the remaining employees cycle or walk to work. What is the probability of each event?
a) A randomly selected employee uses a car or a train
b) A randomly selected employee is a commuter
c) A randomly selected employee uses neither a car nor a train.

answers are: a) 80/140 b) 95/140 c) 45/140

What I don't get is questions a) and b). How are they different? I calculated both of them using P(AorB)=P(A)+P(B)-P(AandB)
so that would be for question a) 32/140+78/140-15/140= 95/140 why do you take off an extra 15/140??

 

[Deleted member 4993]

A company surveyed its 140 employees and determined that 32 commuted by car and 78 by train. Of these commuters, fifteen used both modes of transportation. the remaining employees cycle or walk to work. What is the probability of each event?
a) A randomly selected employee uses a car or a train
b) A randomly selected employee is a commuter
c) A randomly selected employee uses neither a car nor a train.

answers are: a) 80/140 b) 95/140 c) 45/140

What I don't get is questions a) and b). How are they different? I calculated both of them using P(AorB)=P(A)+P(B)-P(AandB)
so that would be for question a) 32/140+78/140-15/140= 95/140 why do you take off an extra 15/140??

This problem is very ill-defined. In a work place - everybody is commuter - unless you have boarding houses in the factory area. So in my opinion, answer to b) should be 140/140.

Looking at the answer, I "surmise" that

for a) - they want you to exclude the peopple who uses both train and car - i.e. they want you to consider those people who uses "only train"( 32-15 = 17) and "only bus" (78 - 15 = 63) - that would be (63+17=) 80.

 

[flyingfreedom]

why do you subtract from both terms? Shouldn't one follow the formula: P(AorB)=P(A)+P(B)-P(AandB)

 

[tkhunny]

It goes to the meaning of the word "or". If "or" means either, but not both, then SK has it correct. This is an "exclusive" or. If "or" is "inclusive", then you have it correct with the formula.

As it was stated, this is an ill-defined question. The question needs work before too much sleep is lost trying to figure out the answers.