The table below shows the employment status of individuals living in a particular town by age group.
Full-time Part-time Unemployed
0-17 26 150 393
18-50 357 56 18
51+ 432 158 172
If a person in this town is selected at random, what is the probability that the individual is unemployed, given that he or she is over 51 years old?
To find the probability of an individual being unemployed given that they are over 51 years old, we need to find the number of unemployed individuals in the 51+ age group and divide it by the total number of individuals in the 51+ age group.
From the table, we see that there are 172 unemployed individuals in the 51+ age group. The total number of individuals in the 51+ age group is 432 + 158 + 172 = 762.
Therefore, the probability that a person is unemployed, given that they are over 51 years old, is 172/762, which simplifies to approximately 0.226, or 22.6%.
To find the probability that an individual is unemployed given that they are over 51 years old, you need to calculate the conditional probability.
First, find the total number of individuals who are over 51 years old:
Total = Full-time + Part-time + Unemployed
= 432 + 158 + 172
= 762
Next, find the number of unemployed individuals who are over 51 years old:
Number of unemployed individuals over 51 = Unemployed
= 172
Now, calculate the probability using the formula:
Probability = (Number of unemployed individuals over 51) / (Total number of individuals over 51)
Probability = 172 / 762
Probability = 0.2254 (rounded to four decimal places)
Therefore, the probability that an individual is unemployed given that they are over 51 years old is approximately 0.2254.
To find the probability that the individual is unemployed given that he or she is over 51 years old, we need to use conditional probability.
Conditional probability is calculated by dividing the number of favorable outcomes by the number of total outcomes.
In this case, the number of favorable outcomes is the number of unemployed individuals who are over 51 years old, which is 172.
The total number of outcomes is the number of individuals who are over 51 years old, which is the sum of the unemployed, full-time employed, and part-time employed in the 51+ age group, which is 172 + 432 + 158.
So, the total number of outcomes is 762.
Therefore, the probability that an individual is unemployed, given that he or she is over 51 years old, is 172/762, which is approximately 0.225 or 22.5%.