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At Tech High there are three math teachers, Mary, Tom, and Alex. All students at Tech High take math, with 21% taking class with Mary, 15% with Tom, and 64% taking class with Alex. Every year 4% of Mary’s students fail, 6% of Tom’s students fail, and 13% of Alex’s student fail. What is the probability that a Tech High student fails math? If needed, round to FOUR decimal places.

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Answer:

The probability that a Tech High student fails math is 0.1006

Step-by-step explanation:

21% students are taking class with Mary.

Every year 4% of Mary’s students fail,

15% students are taking class with Tom

Every year 6% of Tom’s students fail.

64% students are taking class with Alex

Every year 13% of Alex's students fail.

Now we are supposed to find the probability that a Tech High student fails math.

[tex]P(\text{Tech High student fails math}) = P(\text{taking class with Mary})\times P(\text{Mary students fail})+P(\text{taking class with Tom}) \times P(\text{Tom students fail})+P(\text{taking class with Alex}) \times P(\text{Alex student fail})[/tex]

[tex]P(\text{Tech High student fails math}) = 0.21 \times 0.04+0.15 \times 0.06+0.64 \times 0.13[/tex]

[tex]P(\text{Tech High student fails math}) =0.1006[/tex]

Hence the probability that a Tech High student fails math is 0.1006

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