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Use the data in the table below, which shows the employment status of individuals in a particular town by age group.A person from the town is randomly selected; what is the probability that the individual is employed full-time, given that he or sheis between 18 and 49 years of age?Full-timePart-timeUnemployed0-172416437118-2518520314826-34348652735-4958117911850+443162173

Use The Data In The Table Below Which Shows The Employment Status Of Individuals In A Particular Town By Age GroupA Person From The Town Is Randomly Selected Wh class=

Sagot :

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.

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