0:35:59Question 18Not yet answeredMarked out of 6.00Flag questionTipsQUESTION 3PART 1A student is taking a multiple choice test consisting of five questions, each with four options for each question. The student selects the answers at random.a) What is the probability that the student will get at least one question correct?b) Calculate the expected number of questions correct.PART 2A sample of 100 people is selected for a survey, among the questions asked was"Do you like Statistics?" and "Do you live in Wollongong?". Of the 100 people,  80 said they like Statistics, 53 people said they like Statistics and also live in Wollongong(at the same time), 15 people said they don't like Statistics and also don't live in Wollongong (at the same time).a) Find the following probability, P(Likes Statistics | Live in Wollongong)b) Are the events "Likes Statistics" and "Lives in Wollongong" statistically independent?Show your working by typing your answer in the text box below.

A student is taking a multiple choice test consisting of five questions, each with four options for each question. The student selects the answers at random.a) What is the probability that the student will get at least one question correct?b) Calculate the expected number of questions correct.

A student in his exam, selects option C for all 10 multiple choice questions (MCQ). According to statistics, how many questions out of 10, the student will be right?(Format of the exam: 10 MCQ. Each MCQ has 4 answer choices A,B,C,D - out of which 1 choice is right and rest 3 are wrong)Disclaimer: Please do not try this in this quiz !!!Answer choicesSelect only one optionREVISITA) 5B) 2.5C) 2D) 5.50/10 questions attempted

A quiz consists of 10 multiple-choice questions, each with 4 possible answers, only one of which is correct. A student who does not attend lectures on a regular basis has no clue what the answers are, and therefore uses an independent random guess to answer each of the 10 questions. What is the probability that the student gets at least one question right?Let's decide on some notations.Let L be the event that the student gets at least one of the questions right.We'll use R for getting a question right and W for getting it wrong (W is essentially "not R").Given the "tactic" of the student, what is P(R) and P(W)?

(a) [4 marks] A student answers a multiple-choice examination question that offersfour possible answers. Suppose that the probability that he knows the answer tothe question is 0.8 and the probability that he guesses is 0.2. Assume that if thestudent guesses, the probability of selecting the correct answer is 0.25. If the studentcorrectly answers a question, find the probability that he really knew the correctanswer.(b) [5 marks] Suppose the student takes an examination with 3 multiple choice ques-tions. Let X denote the number of questions he gets correct. Assuming that thestudent answers each question independently, determine the probability distributionof X and calculate the expected value of X.(c) [10 marks] Suppose the student takes an examination with 2 multiple choice ques-tions. But this time, he gains confidence every time he knows the answer to a ques-tion. Specifically, if he knows the answer to the current question, then for the nextquestion the probability that he knows the answer becomes 0.9 and the probabilitythat he guesses becomes 0.1. If he does not know the answer to the current ques-tion, then for the next question the probability that he knows the answer and theprobability that he guesses remain 0.8 and 0.2, respectively. Again letting X denotethe number of questions he gets correct, determine the probability distribution of Xand calculate the expected value of X. We can assume the probabilities of knowingthe answer and guessing for the first question are 0.8 and 0.2, respectively.

Exactly 3000 students wrote a multiple-choice test comprising exactly five questions, each question, in turn, having exactly five answer choices, exactly one of which is correct. Every question correctly answered fetches 4 marks and every question incorrectly answered fetches –1 mark. If each student attempted all the questions and the answer choices marked by no two students are the same for all the five questions, then the number of students with a net positive score in the test is at least