74% of the population subscribes to a newspaper 46% of the population subscribe to magazine assuming that these are independent events.

Question

A. Are these events moocher exclusive? Why are why not?
B. Find the probability that a household only subscribes to the newspaper.
C. Find the probability that a household doesn't subscribe to either.
D. Find the probability that a household subscribe to either the newspaper or magazine.

Answer 1

A. No, these events are not mutually exclusive because there can be households that subscribe to both a newspaper and a magazine.

B. To find the probability that a household only subscribes to the newspaper, we need to subtract the probability of subscribing to both from the probability of subscribing to only the newspaper. Since these events are independent, we can multiply the probabilities as follows:

P(Only newspaper) = P(Newspaper) - P(Newspaper and Magazine)
= 74% - (74% * 46%)
= 74% - 34.04%
= 39.96%

Therefore, the probability that a household only subscribes to the newspaper is 39.96%.

C. To find the probability that a household doesn't subscribe to either, we need to subtract the probability of subscribing to either from 100%. Since these events are independent, we can multiply the probabilities as follows:

P(Not subscribing to either) = 100% - P(Newspaper or Magazine)
= 100% - (74% + 46% - 74% * 46%)
= 100% - 60.96%
= 39.04%

Therefore, the probability that a household doesn't subscribe to either is 39.04%.

D. To find the probability that a household subscribes to either the newspaper or magazine, we can add the probabilities of each event:

P(Newspaper or Magazine) = P(Newspaper) + P(Magazine) - P(Newspaper and Magazine)
= 74% + 46% - (74% * 46%)
= 74% + 46% - 34.04%
= 85.96%

Therefore, the probability that a household subscribes to either the newspaper or magazine is 85.96%.