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

Question

B. Find the probability that a household only subscribes to the newspaper.
C. Find the probability that a household doesn't subscribe to either.

Answer 1

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.

Probability of subscribing to both = Probability of subscribing to the newspaper x Probability of subscribing to the magazine.

The probability of subscribing to the newspaper is given as 74%, and the probability of subscribing to the magazine is given as 46%.

Probability of subscribing to both = 74% x 46% = 0.74 x 0.46 = 0.3404.

Thus, the probability of subscribing to only the newspaper = Probability of subscribing to the newspaper - Probability of subscribing to both = 0.74 - 0.3404 = 0.3996.

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 the newspaper or the magazine from 1 (since this includes all possible outcomes).

Probability of subscribing to either the newspaper or the magazine = Probability of subscribing to the newspaper + Probability of subscribing to the magazine - Probability of subscribing to both.

The probability of subscribing to the newspaper is given as 74%, the probability of subscribing to the magazine is given as 46%, and the probability of subscribing to both is 0.3404 (as calculated above).

Probability of subscribing to either the newspaper or the magazine = 74% + 46% - 0.3404 = 0.74 + 0.46 - 0.3404 = 0.8596.

Therefore, the probability that a household doesn't subscribe to either is 1 - Probability of subscribing to either the newspaper or the magazine = 1 - 0.8596 = 0.1404.

Therefore, the probability that a household doesn't subscribe to either is 14.04%.