Probability question on school classes

[Saladsamurai]

Homework Statement

In a high-school graduating class of 100 students, 54 studied math, 69 studied history, and 35 studied both math and history. If 1 of the students is selected at random, find the probability that

(a) the student took math or history;
(b) the student did not take either of these subjects;
(c) the student took history but not math.

Homework Equations

P = n/N

The Attempt at a Solution

Ok. I am thinking that I actually need to figure out how many students took math only and history only (pretty sure this is just algebra).

So I know that there are 54 math students; this must include those who studied both. Thus, the number of students who studied *math only* is 54 - 35 = 19.
Similarly, those who took History only 69 - 35 = 34.

So for (a) P(M U H) = (19 + 34) / 100 = 53/100 ... but this is wrong. Book says 22/25. So I am off to a bad start. What am I screwing up here?

 

[gabbagabbahey]

"or" is an inclusive word, so you also need to include the 35 who took both math and history

 

[Saladsamurai]

I guess an alternative approach to this would be

$P(M\cup H) = P(M) + P(H) - P(M\cap H)$

where M is the math set, H is the History set, etc.​

Just curious as to why my first attempt fails?

EDIT:

"or" is an inclusive word, so you also need to include the 35 who took both math and history

I see. I was wondering about that and had somehow convinced myself that it was exclusive. In general, is "or" inclusive in probability? How about math in general?

 

[gabbagabbahey]

Or is inclusive in math, probability and computer science...The only instance where "or" is exclusive , that comes to mind, is in common everyday conversational usage.

 

[Saladsamurai]

Or is inclusive in math, probability and computer science...The only instance where "or" is exclusive , that comes to mind, is in common everyday conversational usage.

Hence why my waitress never says, "that comes with soup or salad or both."