In a high school graduating class of 100 students, 47 studied mathematics, 61 studied physics, and 25 studied both mathematics and physics. if one of these students is selected at random, find the probability that (a) the student took mathematics or physics. (b) the student did not take either of these subjects. (c) the student took physics but not mathematics. are studying mathematics and physics mutually exclusive events? why or why not?

given,

Probability of student studying math P(M)=

Probability of student studying physicsP(P) =

Probability of student studying both math and physics together P(M∩P) =

a) student took mathematics or physics

P(M∪P) = P(M) + P(P) - P(M∩P)

             = 0.45 + 0.61  - 0.25

             = 0.81

b) student did not take either of the subject

P((M∪P)') = 1 - 0.81

               = 0.19

c) Student take physics but not mathematics

P(P∩M') = P(P) - P(P∩M)

             = 0.61 - 0.25

             = 0.36

studying physics and mathematics is  not mutually exclusive because we can study both the subjects.

b. latent learning (the word "latent" itself means something that exists but isn't obvious, only under certain conditions! )

what is the question because that is not a question.