can i have the final answers with some explanations for this

can i have the final answers with some explanations for this question:

A survey is carried out to find out the percentage of persons affected by a certain disease. Because some people may be inclined to deny being affected by this disease, each person questioned is given a six-faced die and asked to roll it in secret and follow the following rules: if the shown number is 1, the interviewee must answer NO, if the number shown is 6, the interviewee must answer YES and if the result is any other number then the interviewee must say the truth (YES or NO). Since the number shown by the die is not revealed, it is impossible to tell from the given answer if a particular interviewee is affected by the disease or not.

1. Suppose the probability of answering YES in the survey is found to be 2/3, what is the probability of

being affected by the disease?

2. Suppose the probability of being affected by the disease is 3/4. How likely is it that a person who

answers NO in affected by the disease? And a person who answers YES

3. The survey is carried out on 500 persons, 45 of which answer YES. Provide an estimate of the percent-

age of persons affected by the disease among the 500 interviewees.

Solution

Given a dice is rolled, the possible outcomes are 1,2,3,4,5,6

1:No,6:Yes

P(yes)=2/3

P(affected by disease)=1/6*2/3

If P(affected by disease)=3/4

P(answers NO affected by disease)=1/6*3/4

P(answers Yes affected by disease)=1/6*3/4

Given n=500

45 of which answer Yes.

Percentage of persons affected by disease is 45/500=9%.