Probability question - how do I do this question?

Question

A group of 300 students were asked a sensitive question.

Before answering the question, each student secretly rolled a die. If the die indicated 1, 2, or 3 then they were asked to answer the question honestly. If the die indicated 4 or 5 then they were asked to answer "yes" regardless of their true answer. If the die indicated 6 then they were asked to answer "no". This provides perfect anonymity, since it is impossible to tell whether an answer was their own or given by the die. Of the 300 students, a total of 135 answered "yes" using this technique. Based on this sample, what is the estimate of the true proportion of students who would answer "yes" to the actual question?

Answer 1

150 of honest answers.

100 of forced yesses.

50 of forced nos.

135 = [100 of forced yesses] + [35 of honest yesses]

estimate = 35 + (150/2) = 110 honest yesses

Answer 2

Half of the answers are honestly answered. ( 3 out of 6 )

150 of total true answers.

2 out of 6 are yes regardless, need to be removed.

135 -300 *2/6 = 35 are real YES.

So, the answer is 35/150 = 23.33%