Question 953354
p(c) = .7
p(d) = .25


these events are mutually exclusive since she can't stay at home and study and go out to see a movie at the same time.


p(c and d) is therefore equal to 0.


p(c or d) = p(c) + p(d) - p(c and d) = .7 + .25 - 0 = .95.


p(c') is the probability that she won't stay home and study.


p(c') is equal to 1 - p(c) which is equal to 1 - .7 which is equal to .3


since all the probabilities added together must be equal to 1, she has:


p(c) = .7
p(d) = .25
p(c or d) = .95


p(c') = 1 - .7 = .3
p(d') = 1 - .25 = .75
p(c or d)' = 1 - .95 = .05


p(c or d)' means the probability that she will not stay home and study and she will not go out to a movies.   in other words, she'll do something else.


the solution to your problem is:


p(c') = .3 and p(c or d) = .95.