Question

All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?

Answer 1

To find the percent of trainees who passed both tests, we take the lower percentage of passing and consider it as the maximum number of trainees who could have passed both tests.

Step-by-step explanation:

To find the percent of trainees who passed both tests, we need to find the intersection between the trainees who passed the written test and the trainees who passed the flight test.

Let's say there are 100 trainees in total. If 70% of them passed the written test, that means 70 trainees passed. If 80% of them passed the flight test, that means 80 trainees passed.

To find the intersection, we take the lower number, which is 70, as the maximum number of trainees who could have passed both tests. Therefore, 70 trainees passed both tests.

So, the percent of trainees who passed both tests is 70%.

Answer 2

50%

Step-by-step explanation:

Percentage who passed the written test, n(W)=70%

Percentage who passed the flight test, n(F)=80%

Total,
`n(F\cup W)=100`

`n(F\cap W)=`Percentage of those who passed BOTH flying and Written Test.

From set notation,

`n(F\cup W)=n(F)+n(W)-n(F\cap W)\\100=80+70-n(F\cap W)\\100=150-n(F\cap W)\\n(F\cap W)=150-100\\n(F\cap W)=50`

The percentage of the trainees who passed both tests is 50%.