Question

Suppose 83 percent of all people in a sample support global warming, if 74 percent of the people surveyed are women , and 60 percent fit both categories. What is the chance of selecting a person randomly who has neither attributes? a.0.03b.0.39c.0.24d.0.09 Are the two attributes Independent of each other? a.The attributes are Independent because the product of the probability of the two happening simultaneously is equal to the product of the individual probabilities. b.The attributes are not Independent because the product of the probability of the two happening simultaneously is not equal to the product of the individual probabilities.c.That information cannot be deciphered from the problem d.None of the Above

Answer 1

P(A or B) = P(A) + P(B) - P(A & B)

P(supporting global warming) = 0.83

P(women) = 0.74

P(woman and supporting global warming) = 0.60

P(woman or supporting global warming) = 0.83 + 0.74 - 0.60

= 0.97

P(a person randomly who has neither attributes) = 1 - 0.97

= 0.03

P(supporting global warming) x P(woman) = 0.83x0.74 = 0.6142 P(woman and supporting global warming)

Two events are independent if P(A) x P(B) = P(A & B)

b.The attributes are not Independent because the product of the probability of the two happening simultaneously is not equal to the product of the individual probabilities