posterior probability

*Bayesian Statistical Inference

Assume that the chances of a person having a skin disease are 40%. Assuming thatskin creams and drinking enough water reduces the risk of skin disease by 30% andprescription of a certain drug reduces its chance by 20%. At a time, a patient canchoose any one of the two options with equal probabilities. It is given that afterpicking one of the options, the patient selected at random has the skin disease. Findthe probability that the patient picked the option of skin creams and drinking enoughwater using the Bayes theorem.Assume E1: The patient uses skin creams and drinks enough water; E2:The patient uses the drug; A: The selected patient has the skin disease

In probabilistic reasoning for AI, what does the term posterior probability refer to?a)The probability of an event occurring in the future.b)The probability of an event occurring before any evidence is observed.c)The probability of an event occurring given the observed evidence.d)The probability of an event occurring in the absence of any evidence.

Among which of the following mentioned statements can the Bayesian probability be applied?i. In the cases, where we have one eventii. In the cases, where we have two eventsiii. In the cases, where we have three eventsiv. In the cases, where we have more than three events1 pointOnly iv.All i., ii., iii. and iv.ii. and iv.Only ii.

c. Student A tells his professor that he forgot to submit his assignment. From pastexperience, the professor knows that students who finish their assignment on timeforget to submit it 1 in 100 times. He also knows that half the students who have notcompleted their assignments will tell him they forgot to submit. He thinks that 90% ofthe students in his class finished their assignments on time.Using Bayes’ theorem defined in Equation (1) and calculate:P(E Hi) ⋅ P(Hi)P(Hi E) =∑kn=1 P(E Hn) ⋅ P(Hn) Equation (1)i. What is the prior probability that a student forgets to submit his/her assignment?Show how P(E) and P(Hi) are defined to calculate this prior probability. (8 marks)ii. What is the probability that student A is telling the truth, i.e. he/she finished theassignment but forgot to submit it? (5 marks)[13 Marks]