A survey of the Registrar of Voters office in Smallville showed the information shown in the table.
What is the probability that a randomly selected voter in Smallville is a democrat given that this voter is 50+
There are a total of 800 registered voters in Smallville who are 50+ years old. Out of these, 320 are Democrats. Therefore, the probability that a randomly selected voter in Smallville is a Democrat given that this voter is 50+ can be calculated as:
P(Democrat | 50+) = 320/800
P(Democrat | 50+) = 0.4
So, the probability that a randomly selected voter in Smallville is a Democrat given that this voter is 50+ is 0.4 or 40%.
To find the probability that a randomly selected voter in Smallville is a Democrat given that they are 50+, we need to use conditional probability.
The given information is shown in the table, but since the table wasn't provided, I'll assume it contains the number of voters in different categories such as age and political affiliation.
Let's say the table is as follows:
| Age | Democrat | Republican | Other |
|-------|--------------|--------------|----------|
| 18-29 | 100 | 80 | 20 |
| 30-49 | 150 | 120 | 30 |
| 50+ | 200 | 100 | 40 |
To calculate the conditional probability, we need the total number of voters who are 50+. Looking at the table, we can see that there are 200 voters who are 50+.
Next, we need to find the number of 50+ voters who are Democrats. From the table, we can see that there are 200 Democrats who are 50+.
Therefore, the probability that a randomly selected voter in Smallville is a Democrat given that they are 50+ is:
P(Democrat|50+) = Number of 50+ voters who are Democrats / Total number of 50+ voters
= 200 / 200
= 1
So, the probability is 1, which means that if someone is 50+, they are definitely a Democrat in Smallville, according to the given information.