[POTD] The Absent Soccer Fans

[MathBuster Forum]

Fanna Kansal has 30 students in his class. Out of these, 21 students are soccer fans and 9 are not.

Mr. Kansal always asks questions to randomly chosen students in his class. So, if every student is present, the probability of asking a question to a soccer fan is 21/30 = 7/10 and the probability of asking a question to a student who is not a soccer fan is 9/30 = 3/10.

One morning, Mr. Kansal notices that:

• at least one baseball fan was absent,
• at least one non-fan was absent; 
• more than half of his class was present; and
• the probability of asking a question to a soccer fan was 3/4 . 
  

Is there enough information to determine how many students were absent that particular morning? If yes, how many students were absent? If no, explain why not.

Note: As always, it is the solution that matters.