Lubbock, Texas ran a survey and determined that 27% of all households
subscribed to the daily paper, 32% watched the evening news, and 9% did both. If a household is chosen at random, what is the probability that the evening paper was received or the news was watched?
To find the probability that the evening paper was received or the news was watched, we need to use the concept of Union from set theory.
First, let's determine the probability of receiving the evening paper:
Given that 32% of households watched the evening news, the probability of receiving the evening paper is 0.32.
Next, let's determine the probability of watching the news:
Given that 27% of households subscribed to the daily paper, the probability of watching the news is 0.27.
However, we have to make sure to account for the households that did both, as we don't want to count them twice. The probability of both receiving the evening paper and watching the news is 0.09.
To find the probability of either receiving the evening paper or watching the news, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Where A represents the event of receiving the evening paper and B represents the event of watching the news.
P(A or B) = 0.32 + 0.27 - 0.09
P(A or B) = 0.59
Therefore, the probability that a household chosen at random received the evening paper or watched the news is 0.59 or 59%.