A multiple choice question has `n` options, of whlch only one is correct. If a student does home work, then it is sure to identify the correct answer, otherwise answer is choosen at random. Let `E` be the event that student does home work with `P(E)=p` and `F` be the event that student answers question correctly
If the largest set of values of `p` for which relaton `P(E//F)geP(E)` holds is `[a,b]` then

Options

A. `b+a=1`
B. `b+a=1/2`
C. `b-a=1`
D. `b-a=1/2`

Explanation

To solve the problem step by step, we will analyze the events and their probabilities systematically.

### Step 1: Define the Events
Let:
- \( E \): The event that the student does homework.
- \( F \): The event that the student answers the question correctly.
- \( P(E) = p \): The probability that the student does homework.
- \( P(F | E) = 1 \): If the student does homework, they will definitely get the answer correct.
...