John has to take a math quiz. Each quiz consists of 10 questions. For each question the computer randomly chooses 1 question from a question set containing 4 possible questions. John understands the material for 7 of the 10 questions well enough that he will be able to answer correctly, no matter which question is chosen from the question set. For 1 of the questions, John doesn’t really understand the concept and will have to guess at the answer no matter which question is chosen from the question set. For each of the other 2 questions on the quiz, John does have a basic understanding of the concept, and would know the right answer for 3 of the questions in the question set, but 1 of the possible questions has a complication that John doesn’t understand, so he would have to guess at the answer.Every question in the question database has 5 answer choices, so whenever John guesses at a question he randomly chooses 1 of 5 answers. Of course, only 1 of the 5 is the right answer. Every question on the quiz is worth 1 mark, so the quiz is out of 10 marks. Assume that John will get right every question he knows how to answer. That is, he does the quiz carefully, not making any arithmetic errors or clicking a wrong answer by accident, or forgetting to save an answer.

 

(a) Under what circumstances will John get a mark less than 8 when he takes this quiz?

(b) Find the probability that John will get at least 8 out of 10 on the quiz

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Status NEW Posted 22 Apr 2017 06:04 AM My Price 9.00

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