Question

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.

Answer 1

The probability that a Tech High student fails math is 0.1006

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.

`P(\text{Tech High student fails math}) = P(\text{taking class with Mary})* P(\text{Mary students fail})+P(\text{taking class with Tom}) * P(\text{Tom students fail})+P(\text{taking class with Alex}) * P(\text{Alex student fail})`

`P(\text{Tech High student fails math}) = 0.21 * 0.04+0.15 * 0.06+0.64 * 0.13`

`P(\text{Tech High student fails math}) =0.1006`

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