The probability that a firefighter has a college degree given that they are in the Special Units Division is 2/5.
The conditional probability is the happening of an event, when the probability of occurring of other event is given.
The probability of event A, given that the event B is occurred,
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
A total of 20% of a fire department's firefighters are in the Special Units Division. Let consider it as event B. Thus,
[tex]P(B)=\dfrac{20}{100}\\P(B)=\dfrac{1}{5}[/tex]
A total of 8% of the department's firefighters are in the Special Units Division AND have a college degree. Let having college degree is event A. Thus,
[tex]P(A\cap B)=\dfrac{8}{100}\\P(A\cap B)=\dfrac{2}{25}[/tex]
Thus, the probability that a firefighter has a college degree given that they are in the Special Units Division is,
[tex]P(A|B)=\dfrac{\dfrac{2}{25}}{\dfrac{1}{5}}\\P(A|B)={\dfrac{2}{5}}[/tex]
Thus, the probability that a firefighter has a college degree given that they are in the Special Units Division is 2/5.
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