Question

17% of the households in a community donate to the local public television station. Among households that donate to the public television station, 30% donate to the local public radio station. Among households that do not donate to the public television station, only 5% donate to the public radio station. Answer the following for a randomly selected household in the community” What is the probability a household does not donate to the public television station if the household donates to the public radio station?

Answer 1

P(donate to local public telivision station) = 0.17

P(donate to local radio station | donate to local telivision station) = 0.3

P(donate to local radio station | doesn't donate to local telivision station) = 0.05

P(donate to local radio station) = P(donate to local radio station | donate to local telivision station) * P(donate to local telivision station) + P(donate to local radio station | doesn't donate to local telivision station) * P(doesn't donate to local telivision station)

                                                  = 0.3 * 0.17 + 0.05 * (1 - 0.17)

                                                  = 0.0925

P(doesn't donate to local telivision station | donate to local radio station) = P(donate to local radio station | doesn't donate to local telivision station) * P(doesn't donate to local telivision station) / P(donate to local radio station)

                                                 = 0.05 * (1 - 0.17) / 0.0925

                                                 = 0.4486 (ans)