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.
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.
To find the requested probabilities, we need to use the concept of independent events.
Let's denote the event of subscribing to a newspaper as "N" and the event of subscribing to a magazine as "M."
Given:
P(N) = 74% = 0.74 (probability of subscribing to a newspaper)
P(M) = 46% = 0.46 (probability of subscribing to a magazine)
We know that the events of subscribing to a newspaper and subscribing to a magazine are independent. Therefore, we can use the multiplication rule for independent events:
P(N and M) = P(N) * P(M)
A. To find the probability that a household only subscribes to the newspaper:
This means that the household subscribes to the newspaper (event N) but does not subscribe to the magazine (event M).
P(N and not M) = P(N) * P(not M)
Since the events are independent, P(not M) = 1 - P(M)
P(N and not M) = P(N) * (1 - P(M))
B. To find the probability that a household doesn't subscribe to either:
This means that the household does not subscribe to the newspaper (event N) or the magazine (event M).
P(not N and not M) = P(not N) * P(not M)
Since P(not N) = 1 - P(N) and P(not M) = 1 - P(M), we can substitute these values:
P(not N and not M) = (1 - P(N)) * (1 - P(M))
C. To find the probability that a household subscribes to either the newspaper or the magazine:
This means that the household subscribes to the newspaper (event N) or the magazine (event M).
P(N or M) = P(N) + P(M) - P(N and M)
Since the events N and M are independent, P(N and M) = P(N) * P(M), so we can substitute this value:
P(N or M) = P(N) + P(M) - P(N) * P(M)
Now we can plug in the given values to calculate the probabilities.