binomial probability distribution question #5
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. What is the probability that she will get at least 4 questions correct?
The student determines the correct answer by choosing a ball from a box that has 4 balls marked with the options A, B, C and D. The probability that a randomly picked ball has the right answer is 0.25.
In a test that has 5 questions the probability that at least 4 questions are right has to be determined. This is the same as the probability that only one question is wrong or none of the questions are wrong. The probability of choosing a ball with a wrong answer is 0.75.
The probability that none of the questions is wrong is (0.25)^5. The probability that only one question is wrong is 5C1*(0.25)^4*(0.75)
Adding the two (0.25)^5 + 5C1*(0.25)^4*(0.75) = 0.015625
This gives the probability that she gets at least 4 correct answers as 0.015625