Question

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

To find the probability that a household only subscribes to the newspaper, we need to subtract the probability of subscribing to both the newspaper and magazine from the probability of subscribing to just the newspaper.

Let A be the event that a household subscribes to the newspaper, and B be the event that a household subscribes to the magazine.

P(A) = 0.74 (given)

P(B) = 0.46 (given)

Since the events are independent:

P(A and B) = P(A) * P(B) = 0.74 * 0.46 = 0.3404

To find the probability that a household only subscribes to the newspaper, we subtract P(A and B) from P(A):

P(only newspaper) = P(A) - P(A and B) = 0.74 - 0.3404 = 0.3996

Therefore, the probability that a household only subscribes to the newspaper is 0.3996.

To find the probability that a household doesn't subscribe to either the newspaper or magazine, we take the complement of the event that a household subscribes to either the newspaper or magazine:

P(neither) = 1 - P(A or B)

Since the events are independent:

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

P(A or B) = 0.74 + 0.46 - 0.3404 = 0.8596

P(neither) = 1 - 0.8596 = 0.1404

Therefore, the probability that a household doesn't subscribe to either the newspaper or magazine is 0.1404.

Lastly, to find the probability that a household subscribes to either the newspaper or magazine, we can add P(A) and P(B) and then subtract P(A and B):

P(n ewspaper or magazine) = P(A) + P(B) - P(A and B)

P(newspaper or magazine) = 0.74 + 0.46 - 0.3404 = 0.8596

Therefore, the probability that a household subscribes to either the newspaper or magazine is 0.8596.