4. Dan and Phil are preparing to host a party. They want to have a set of cornhole boards for guests to play. They have ordered a cornhole set online. There is an 84% chance that the cornhole set will arrive in time for the party. If the cornhole set arrives in time, then Annie (who loves to play the game) will attend with a probability 0.95. In the event there is no cornhole, Annie will not attend Dan and Phil's party with a probability of 0.27. a) Represent this situation with a tree diagram. Label the parts clearly. b) What is the probability there is no cornhole? c) What is the probability Annie attends Dan and Phil's party?
4. Dan and Phil are preparing to host a party. They want to have a set of cornhole boards for guests to play. They have ordered a cornhole set online. There is an 84% chance that the cornhole set will arrive in time for the party. If the cornhole set arrives in time, then Annie (who loves to play the game) will attend with a probability 0.95. In the event there is no cornhole, Annie will not attend Dan and Phil's party with a probability of 0.27. a) Represent this situation with a tree diagram. Label the parts clearly. b) What is the probability there is no cornhole? c) What is the probability Annie attends Dan and Phil's party?
Transcribed Image Text:4. Dan and Phil are preparing to host a party. They want to have a set of cornhole boards for guests to play. They
have ordered a cornhole set online. There is an 84% chance that the cornhole set will arrive in time for the
party. If the cornhole set arrives in time, then Annie (who loves to play the game) will attend with a probability
0.95. In the event there is no cornhole, Annie will not attend Dan and Phil's party with a probability of 0.27.
a) Represent this situation with a tree diagram. Label the parts clearly.
b) What is the probability there is no cornhole?
c) What is the probability Annie attends Dan and Phil's party?
d) Given that Annie did attend the party, what is the probability there was cornhole at the party?
e) Is whether Annie attends the party independent of whether there is cornhole? Mathematically justify your
answer.
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