A recent GSS asked subjects whether they are a member of an environmental group and whether they would be very willing to pay much higher prices to protect the environment. Table 4.4 shows results.

(a) Estimate the probability that a randomly selected American adult is a member of an environmental group.

(b) Show that the estimated probability of being very willing to pay much higher prices to protect the environment is (i) 0.312, given that the person is a member of an environmental group, (ii) 0.086, given that the person is not a member of an environmental group.

(c) Show that the estimated probability that a person is both a member of an environmental group and very willing to pay much higher prices to protect the environment is 0.027 (i) directly using the counts in the table, (ii) using the probability estimates from

(a) and (b).

(d) Show that the estimated probability that a person answers yes to both questions or no to both questions is 0.862.