Problem Solving

I would like clarification in answering probability problems. As the two questions below indicate, there are different methods of getting the probability:

Example 1
A city survey found that 47% of teenagers have a part time job. Of those
teenagers, 78% also plan to attend college. If a teenager is chosen at
random what is the probability that he/she has a part time job and plans
to attend college?

Answer:
(.47)(.78) = .3666
Answer: 37% (to the nearest percent)

Example 2
In a school, 14% of students take drama and computers, and 67% take
computer class. What is the probability that a student taking computers
also takes drama?

Answer:
.14 ÷ .67 = .2090
Answer: 21% (to the nearest percent)

*source: https://www.vkg.werro.ee/aivar/toen/kordamine.htm

What elements of the question would help in determining the type of solution to be used?

Hi, in my case I always use this table:


Att. College No Att. College TOTAL

Part Time 36% 11% 47%

Full Time X% Y% 53%

TOTAL 36% + X 11% + Y% 100%


36% is the 78% of 47%

The first question is asking how many students out the whole 100% are will attend college.
So, there you have 100% or 100 students (to make things simpler) and you're told that 47/100 are part-time students and 78/100*(47/100) are part-time and will go to college, so you just need to calculate this amount-->3666/10000=0.3666%
And that's your answer.

The second problem tells you that 14/100 of students take drama and computers, and 67/100 take computer class. So the probability that a student taking computer class also takes drama would be 14 students out 67 OR 14/67~21%

So, the two questions are a bit different, this is why solutions are different as well.