22. A professor always gives either a fast-paced lecture or a moderately-paced lecture. Also, she has coffee at breakfast, on the average, 3 out of 4 days that she gives a lecture. If she has coffee, her lecture is fast-paced with probability 0.8. However, on momings with no coffee, her lecture is moderately-paced with probability 0.4. Suppose we know that she has given a moderately-paced lecture. What is the probability that she did not have coffee? (A) (B) (C) (D) (E)
and use the graph to guess the value of the integral
. Then evaluate the integral to confirm your guess.