Question

A survey asked subjects whether they are a member of an environmental group and whether they would be very willing to pay higher prices to protect the environment. The results are shown in the table below. For a randomly selected​ adult, find the probabilities specified in parts​ (a) through​ (d).

Pay Higher Prices (GRNPRICE)

Yes No Total

Environmental Yes 31 63 94

Group Member No 88 931 1019

(GRNGROUP) Total 119 994 1113

a. Estimate the probability of being a member of an environmental group.

​P(GRNGROUP)=

Estimate the probability of being willing to pay higher prices to protect the environment.

​P(GRNPRICE)=

b. Estimate the probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment.

​P(GRNGROUP and GRNPRICE)=

c. Given the probabilities in​ (a), calculate the probability in​ (b) if the variables were independent.

​P(GRNGROUP and GRNPRICE)=

  

d. Estimate the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment. Do this directly using the counts in the table.

P(GRNGROUP or GRNPRICE)=

Estimate the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment. Do this by applying the appropriate probability rule to the estimated probabilities found in​ (a) and​ (b).

​P(GRNGROUP or GRNPRICE)=

Answer 1

	GRNprice yes	GRNprice No	total
GRNgroup yes	31	63	94
GRNgroup no	88	931	1019
total	119	994	1113

a)P(GRNGROUP) = 94/1113= 0.0844 or 8.4456%
  
P(GRNPRICE)=119/1113= 0.1069 or 10.6918%
  
b)​P(GRNGROUP and GRNPRICE)=31/1113= 0.0278 or 2.7853%

c)

if the variables were independent.

​P(GRNGROUP and GRNPRICE)=P(GRNGROUP)*P(GRNPRICE) = 0.0844*0.1069 = 0.00903 or 0.9030%

d) by countin rule,

P(GRNGROUP or GRNPRICE)=(31+88+63)/1113=   16.35%

by  probability rule

P(GRNGROUP or GRNPRICE)=P(GRNGROUP)+P(GRNPRICE)-P(GRNGROUP and GRNPRICE) = 8.4456%+10.5918%-2.7853% = 16.35%