Given:
Given a table of data
Required: Probability that an individual is employed full time, given that he or she is between 18 and 49 years of age.
Explanation:
Let A be the event " The individual is employed full time" and B be the event "He or she is between 18 and 49 years of age".
Then
[tex]\begin{gathered} P(A)=\frac{\text{ Number of individuals employed full time}}{T\text{otal number of individuals}} \\ =\frac{1581}{3191} \end{gathered}[/tex]and
[tex]\begin{gathered} P(B)=\frac{\text{ Number of individuals between the age 18 and 49}}{\text{ Total number of individuals}} \\ =\frac{1854}{3191} \end{gathered}[/tex]Probability of individuals employed full time and aged between 18 and 49
[tex]\begin{gathered} =P(A\cap B) \\ =\frac{185+348+581}{3191} \\ =\frac{1114}{3191} \end{gathered}[/tex]To find P(A/B).
By using the conditional probability,
[tex]\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ =\frac{1114}{1854} \end{gathered}[/tex]Final Answer: Probability that an individual is employed full time, given that he or she is between 18 and 49 years of age is 1114/1854.