Final answer:
The question involves calculating various probabilities from given survey data about US economic opinions and party affiliations. These include the probability of being a Democrat, thinking the economy is the same, and various conditional probabilities between these two events.
Step-by-step explanation:
To answer the question about probability from the provided data, first we need to determine the total number of adults surveyed, which is the sum of all individuals with their respective partisan affiliations and opinions on the economy. Adding up the numbers of Republicans, Democrats, and those with no specific affiliation across their views on the economy (Better, Same, Worse), we get a total of 651 adults.
The probability that a randomly selected adult is a Democrat, P(Democrat), is calculated by dividing the number of Democrats by the total number of adults surveyed. Similarly, P(Same) is the probability that an adult thinks the economy is the same, calculated by dividing the number of adults with that opinion by the total surveyed.
Conditional probability is then used for P(Same|Democrat) which is the probability that an adult thinks the economy is staying the same given that they are a Democrat, and P(Democrat|Same) which is the probability that an adult is a Democrat given that they think the economy is staying the same.
P(Democrat and Same) denotes the joint probability that a randomly selected adult is a Democrat who thinks the economy is staying the same, which is found by dividing the number of Democrats who think the economy is the same by the total number of adults.
The calculations are as follows:
- Total number of adults: 651
- P(Democrat): 236 / 651
- P(Same): 281 / 651
- P(Same|Democrat): 87 / 236
- P(Democrat|Same): 87 / 281
- P(Democrat and Same): 87 / 651
To conclude, these probabilities reflect the distribution of party affiliation and economic perceptions among the surveyed group.