74% of the population subscribes to a newspaper 46% of the population subscribe to magazine assuming that these are independent events.
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.
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%.
A. No, these events are not mutually exclusive. Two events are mutually exclusive if they cannot both occur at the same time. In this case, it is possible for a household to subscribe to both a newspaper and a magazine, as they are independent events.
B. 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 magazine from the probability of households that only subscribe to the newspaper.
The probability of subscribing to both the newspaper and magazine can be calculated by multiplying the individual probabilities:
P(newspaper and magazine) = P(newspaper) * P(magazine)
= 0.74 * 0.46
The probability of only subscribing to the newspaper is then:
P(only newspaper) = P(newspaper) - P(newspaper and magazine)
= 0.74 - (0.74 * 0.46)
C. To find the probability that a household doesn't subscribe to either, we need to subtract the probability of households that subscribe to either the newspaper or magazine from 1.
P(no subscription) = 1 - P(newspaper or magazine)
Since the events are independent, we can calculate the probability of subscribing to either the newspaper or magazine as:
P(newspaper or magazine) = P(newspaper) + P(magazine) - P(newspaper and magazine)
= 0.74 + 0.46 - (0.74 * 0.46)
Then the probability of not subscribing to either is:
P(no subscription) = 1 - (0.74 + 0.46 - (0.74 * 0.46))
D. To find the probability that a household subscribes to either the newspaper or magazine, we can use the formula:
P(newspaper or magazine) = P(newspaper) + P(magazine) - P(newspaper and magazine)
= 0.74 + 0.46 - (0.74 * 0.46)