make a table as shown below.\
]
junior senior total
male 18 7 25
female 10 5 15
total 28 12 40
there are 28 juniors out of a total of 40 so the probability of a student, selected at random, of being a junior is 28/40.
there are 25 males out of a total of 40 so the probability of a student, selected at random, of being a male is 25/40.
there are 28 juniors out of a total of 40, so the probability of a student, selected at random, of being a junior is 28/40.
there are 15 females out of a total of 40, so the probability of a student, selected at random, of being a female is 15/40.
the total is 28 + 15 = 43 out of 40, but .....
10 of those are both a female and a junior.
as such, they are being double counted, 10 as a junior and 10 as a female.
to avoid the double counting, you have to subtract 10 from the total to get a total of 28 + 15 - 10 = 33 that are either a junior or a female.
the formulas take care of this.
let a = the probability of being a junior.
let b = the probability of being a female.
the formula states that p(a or b) = p(a) + p(b) - p(a and b)
that becomes 28/40 + 15/40 - 10/40 = (28 + 15 - 10) / 40 = 33/40.