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]

Apply Bayes Theorem to solve the following problem: Consider a set of patients coming for treatment in a certain clinic. LetA denote the event that a "Patient has heart disease" and B the event that a "Patient is having high blood pressure(BP)."It isknown from experience that 10% of the patients entering the clinic have heart disease and 5% of the patients are having highBP. Also, among those patients diagnosed with heart disease, 7% are having high BP. Given that a patient with high BP, whatis the probability that he will have heart disease

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 a school, 30 % of the students study math and science, 70 % of the students study science. What is the probability of students studying math, given that the student is already studying science.a42.8%42.8%b23.33%23.33%c40%40%d63.8%63.8%

Jamie wakes up late on average 1 days out of every 5. If Jamie wakes up late, the probability that she is late for school is 80%. If Jamie doesn't wake up late the probability that she is late for school is 35%. Create a tree diagram by entering the percentages and then calculate the percent chance that Jamie gets to school on time. Enter your answers as a decimal or fraction between 0 and 1. Late On time Late On time Late On time A B C D E F Wake up Get to School [Graphs generated by this script: setBorder(0);initPicture(-8.3,5.5);strokewidth = '2';marker = 'arrow';line([-8,0], [-3,2]);line([-8,0], [-3,-2]);line([0,2], [2,3]);line([0,2], [2,1]);line([0,-2], [2,-1]);line([0,-2], [2,-3]);text([-1.7,2], 'Late');text([-1.6,-2], 'On time');text([4,3], 'Late');text([4,1], 'On time');text([4,-1], 'Late');text([4,-3], 'On time');fontweight = 'bold';text([-6,1.5], 'A');text([-6,-1.5], 'B');text([.7,2.8], 'C');text([.7,1.3], 'D');text([.7,-1.3], 'E');text([.7,-2.9], 'F');text([-1.6,4], 'Wake up');text([4,4], 'Get to School');] Place your percentages here: C: A: D: B: E: F: The percent chance (as a decimal) that Jamie gets to school on time:

A student, Kevin, has handed in all her coursework for CS2114, and wants to workout the chance she will get a distinction in CS2114. She asked 300 students whohave had distinctions in the past, and 100 of them said they handed in all theircoursework. She then asked 600 students who didn’t get distinctions in the past,and only 50 of them said they handed in all their coursework. Past experience showsthat only 15% of students who take CS2114 get distinctions(a) Calculate the prior probability of someone handing in all their coursework.(b) Using this prior and the information above, calculate using Bayes’ rule whatthe probability is that she will get a distinction?(c) If she didn’t hand in all her coursework what is the probability of getting adistinction?