Question: The figure is a Venn diagram with some probabilities of events marked on it. In addition to the values marked on the diagram it is the case that P [B] = 0.4 and P[C / A] = 0.8.

a) Finish filling in the probabilities on the diagram.

b) Use the probabilities on the diagram (and your answers to (a)) and evaluate P[A and B]

c) Use the probabilities on the diagram and evaluate P[B / C]

d) Based on the information provided here, are the events B, C independent events?

e) Based on the information provided here, are the events A, C mutually exclusive events?