Please solve a and d Problem #4. (10 points) Suppose you are taking a multiple c
ID: 3180243 • Letter: P
Question
Please solve a and d Problem #4. (10 points) Suppose you are taking a multiple choice test for which you have mastered 80% of the material. Assume this means that you have a 0.8 chance of knowing the answer to a random test question and that if you don't know the answer to a question then you will randomly select an answer among the five answep choices (note this means you will likely correctly answer some of the questions you do know the answer to). Finally, assume that this holds for each question, independent of the others. a) (3 points) what is your expected score (as a percent) on the exam? ECA) np Let p be the probability of getting a random question correct (note: this should belyour answer to part (a)). You make express your answers to parts b, c, and d using the letter pExplanation / Answer
a. For each question, if the answer is known then 0.8 marks can be scored and if the answer is not known then random answer chosen can be correct with prob 1/5 and 0.2 is the prob. that the answer is not not known.
(1-0.8)*1/5=0.2*0.2=0.04 marks can be scored.
Hence expected percent obtained in the test = 0.8 + 0.04 = 0.84
d. As the questions are independent and expected score does not depend on number of questions, it does not really matter if the number of questions are 10 or 100. But with more number of questions, the chance of randomly choosing correct answers when correct answer is not known is more.
E(random correct | 10 qsns) = 0.04*10=0.4 <1. SO, 8 correct out of 10, prob - 80%
E(random correct | 100 qsns) = 0.04*100 = 4. So, 84 correct out of 100. prob = 84%