The equation of probability, P, that represents a randomly selected student from this class takes Consumer Education, French, or both are: [tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex] .
Given :
In a freshman high school class of 80 students, 22 students take Consumer Education, 20 students take French, and 4 students take both.
Given that students take Consumer Education: n(C) = 22
The students that take French: n(F) = 20
The students that take both: [tex]\rm n(C\cap F) = 4[/tex]
Total Students: n(S) = 80
Students that take Consumer, French, or both:
[tex]\rm n(C\cup F) = n(F) + n(C) - n(C\cap F)[/tex]
[tex]\rm n(C\cup F) = 20 + 22 - 4[/tex]
[tex]\rm Probability = \dfrac{Favourable \;Outcomes}{Total \; Outcomes}[/tex]
[tex]\rm Probability = \dfrac{n(C\cup F)}{n(S)}[/tex]
[tex]\rm Probability = \dfrac{20 + 22 - 4}{80}[/tex]
[tex]\rm Probability = \dfrac{20}{80} + \dfrac{22}{80} -\dfrac{ 4}{80}[/tex]
[tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex]
Therefore, the correct option is D).
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