What's the probability that the student will pass the exam by following her strategy?
A student is taking a multiple choice exam in which each question has 4 choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place 4 balls (marked A, B, C and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are 5 multiple choice questions on the exam. Suppose that the exam has 50 multiple choice questions and 30 or more correct answers is a passing score.
A student is taking a multiple choice exam in which each question has 4 choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place 4 balls (marked A, B, C and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are 5 multiple choice questions on the exam. Suppose that the exam has 50 multiple choice questions and 30 or more correct answers is a passing score.
1 Answer
roughly
Explanation:
We start with a relation that talks about binomial probability:
We have
The probability of getting an answer right by guessing is
A passing grade is
The probability of getting a passing score is:
Instead of summing all this up, I'll use this online calculator tool:
http://stattrek.com/online-calculator/binomial.aspx
We take the box labeled