A history teacher has given her class a list of seven essay questions to study b

Question

A history teacher has given her class a list of seven essay questions to study before the next test. The teacher announced that she will choose four of the seven questions to give on the test, and each student will have to answer three of those four questions. Suppose that a student has enough time to study only five questions. What is the probability that the student will have to answer a question that he or she did not study? That is, what is the probability that the four questions on the test will include both questions that the student did not study?

Explanation / Answer

Each student studies 5 out of 7 test .p = 5/7 = .714

P( student 4 questions will include the question he did not study)

= 4C2 (.714^2)(1-.714)^2 = .2510

So, 25.10% probability that such an event will happen

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