Calculation practice: Law of total probability. The survey in the previous problem was conducted on men as well: 34% say Brussels sprouts are “very repulsive,” 19% say that they are “somewhat repulsive,” 38% are “indifferent,” 8% say they are “somewhat delicious,” and 1% claim they are “especially delicious.” Assume that in a given population, 52% of the adults are women. Use the following steps to build a probability tree and calculate the probability that a random adult says that Brussels sprouts are somewhat delicious or especially delicious using the law of total probability.

a. What is the probability that a randomly chosen adult is a man? What is the probability that a randomly chosen adult is a woman? Draw the first part of the probability tree for these two events.

b. What is the probability that a man says that Brussels sprouts are somewhat delicious or especially delicious?

c. Write (b) as a shorthand probability statement. (b) can also be stated as: What is the probability that a randomly chosen adult says that Brussels sprouts are somewhat delicious or especially delicious, given that he is a man?

d. What is the probability that a woman says that Brussels sprouts are somewhat delicious or especially delicious?

e. Complete the probability tree for the events in parts (c) and (d).

f. Apply the law of total probability to determine the probability that a random adult says that Brussels sprouts are somewhat delicious or especially delicious.