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

Answer:

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%.