A test has five multiple-choice questions. Each question has 4 answer choices, of which 1 is correct answer and the other 3 are incorrect. Suppose that you guess all the answers. a) How many ways are there to answer the 5 questions? b) What is the probability of getting all 5 questions right? c) What is the probability of getting exactly 4 questions right and 1 wrong? d) What is the probability of doing well (getting at least 4 right)?
Accepted Solution
A:
Answer:a) There are 1024 ways to answer the 5 questionsb)The probability is 0.000976c) The probability is 0.014648d) The probability is 0.015624Step-by-step explanation:The number of ways to answer the 5 questions can be calculate as a rule of multiplication in which we have 4 answers for every questions, as: 4 * 4 * 4 * 4 * 4 = 10241st question 2nd 3rd 4th 5thThen there are There are 1024 ways to answer the 5 questions.On the other hand, the probability of get one question right is [tex]\frac{1}{4}[/tex] or 0.25. Because there is only one answer correct from 4 possibles answers.At the same way the probability of gt one question wrong is 3/4 or 0.75. Because there are 3 answers incorrect from 4 possible choices.So, the probability of get 5 questions right, is the multiplication of probabilities of get the right answer in every question:P= 0.25*0.25*0.25*0.25*0.25=0.000976For calculate the probability of getting exactly 4 questions right and 1 wrong, we have five events with their respective probabilities:1. The wrong answer is the first one: P=0.75*0.25*0.25*0.25*0.25=0.0029292. The wrong answer is the second one: P=0.25*0.75*0.25*0.25*0.25=0.0029293. The wrong answer is the third one: P=0.25*0.25*0.75*0.25*0.25=0.0029294. The wrong answer is the fourth one: P=0.25*0.25*0.25*0.75*0.25=0.0029295. The wrong answer is the fifth one: P=0.25*0.25*0.25*0.75*0.25=0.002929So the probability of getting exactly 4 questions right and 1 wrong is the sum of probabilities of all the event mentioned:P=0.002929+0.002929+0.002929+0.002929+0.002929P=0.014648Finally the probability of doing well is the probability of having exactly 4 questions right and 1 wrong plus the probability of getting all 5 questions right:P=0.014648+0.000976P=0.015624