amit is going to guess on all 20 questions of his multiple - choice test. each question on the test has 4…
amit is going to guess on all 20 questions of his multiple - choice test. each question on the test has 4 answer options, and only one is correct. what is the best prediction for the number of questions that amit will answer correctly? choose 1 answer: a exactly 5 questions b close to 5 questions but probably not exactly 5 questions c exactly 80 questions d close to 80 questions but probably not exactly 80 questions
Answer
Explanation:
Step1: Calculate probability of correct answer
The probability of getting a single - multiple - choice question correct by guessing is $p=\frac{1}{4}$ since there is 1 correct option out of 4.
Step2: Use expected - value formula
The expected value $E(X)$ of the number of correct answers in $n$ independent trials (here $n = 20$ questions) is given by $E(X)=n\times p$. Substitute $n = 20$ and $p=\frac{1}{4}$ into the formula: $E(X)=20\times\frac{1}{4}=5$. But this is just the expected value. In a real - life situation of guessing, we are likely to be close to 5 questions correct but not exactly 5 questions due to the random nature of guessing.
Answer:
B. Close to 5 questions but probably not exactly 5 questions