Please help
Diane is looking at her collection of e-Books. She has worked out that
60% of her e-Books were downloaded from Company A, 68% are works
of fiction, and 36% are works of fiction that were downloaded from
Company A. When Diane selects one of her e-Books at random, let the
event that it was downloaded from Company A be A and the event that
it is a work of fiction be F.
a. Draw a Venn diagram to represent the information you have been
given. (As always, be sure to write the probabilities in your diagram
and in your work as decimals, not percentages.)
b. Complete your Venn diagram by writing on it any additional relevant
probabilities.
c. When Diane selects one of her e-Books at random, what is the
probability that it is neither a work of fiction nor was downloaded
from Company A?
d. If Diane randomly selects a work of fiction, what is the probability
that it was downloaded from Company A?
e. If Diane randomly selects a book that was downloaded from
Company A, what is the probability that it is not a work of fiction?
f. What are the values of P(A), P(F), and P A F∩ )?
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g. Use your answers to Part e to decide whether the events A and F are
independent. Be sure to show any calculation that leads to your
answer.