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.
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%.
To find the probability that a household only subscribes to the newspaper, we need to subtract the probability of households that subscribe to both the newspaper and the magazine from the probability of households that subscribe only to the newspaper.
Let's denote:
N = Probability of subscribing to the newspaper
M = Probability of subscribing to the magazine
The probability that a household subscribes only to the newspaper is given by:
P(N only) = P(N) - P(N and M)
Given that 74% of the population subscribes to a newspaper (N = 0.74) and 46% of the population subscribes to a magazine (M = 0.46), the probability of households that subscribe to both the newspaper and the magazine is given by P(N and M) = N * M.
So, the probability that a household only subscribes to the newspaper is:
P(N only) = P(N) - P(N and M)
= N - N * M
= 0.74 - (0.74 * 0.46)
= 0.74 - 0.3404
= 0.3996
≈ 0.4
Therefore, the probability that a household only subscribes to the newspaper is approximately 0.4 or 40%.
To find the probability that a household doesn't subscribe to either the newspaper or the magazine, we need to find the complement of the probability that a household subscribes to at least one of them.
Let's denote:
S = Probability of subscribing to either the newspaper or the magazine
The probability that a household doesn't subscribe to either is given by:
P(Don't subscribe to either) = 1 - P(S)
Now, since the events are assumed to be independent, the probability of subscribing to either the newspaper or the magazine is given by:
P(S) = P(N or M) = P(N) + P(M) - P(N and M)
Given that N = 0.74, M = 0.46, and P(N and M) = N * M, we can find P(S):
P(S) = P(N) + P(M) - P(N and M)
= 0.74 + 0.46 - (0.74 * 0.46)
= 0.74 + 0.46 - 0.3404
= 0.8596
So the probability that a household doesn't subscribe to either the newspaper or the magazine is:
P(Don't subscribe to either) = 1 - P(S)
= 1 - 0.8596
= 0.1404
≈ 0.14
Therefore, the probability that a household doesn't subscribe to either the newspaper or the magazine is approximately 0.14 or 14%.