In: Statistics and Probability
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?
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)