SOLUTION: A student is taking a multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has
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Question 1190719: A student is taking a multiple-choice exam in which each question has four 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 four balls (marked A,B,C,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 six multiple-choice questions on the exam.
What is the probability that she will get at least five questions correct? Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
A student is taking a multiple-choice exam in which each question has four 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 four balls (marked A,B,C,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 six multiple-choice questions on the exam.
What is the probability that she will get at least five questions correct?
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This many-words description means simple thing: for any multiple-choice question,
the answer is selected randomly among four possibilities;
so, the probability of getting a correct answer is = 0.25, while the probabiliy
of getting incorrect answer is = 0.75 for each single multiple choice question.
And the answers to different multiple-choice questions are independent each from another.
It is a typical binomial distribution situation. The formula for the probability to get 5 or more correct answers is
P = P(5) + P(6) = + =
= 0.004639. ANSWER
