statistics - probability of events given data

You invite your friends Etienne and Fae to see a movie. There is a .2 probability that Etienne will not go to see the movie, a .15 probability that Fae will not go to see the movie, and a .05 probability that both will not go to see the movie. What is the probability that

a) either or both will not go to see the movie?

b) at least one of Etienne or Fae will go see the movie?

c) what is the probability that either just Etienne or just Fae will go see the movie (but not both)?

For part a) I did $0.2+0.15-0.05=0.3$

for part b) I'm thinking it will be the compliment of part a) so $1-0.3=0.7$

for part c) I'm struggling to figure out how to calculate this

are my answers so far correct? any hints for c? thanks

Answer

Guide:

• Part $a$ looks fine.




• Part $a$ is describing the event that at least $1$ will not watch the movie. Its complement is both will watch the movie which is not part $b$ is asking for.





• For part $b$, the complement of at least one will watch the movie is none will watch the movie. Note that we are given the probability that none will watch the movie. Just use $1$ to subtract that.




• Hint for part $c$, in part $b$, we know the probability that at least one will watch the movie. We have to subtract the probability that both wil watch the movie. You might like to refer to the second point.