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Nov 2014 p62 q4
2552
Sharik attempts a multiple choice revision question on-line. There are 3 suggested answers, one of which is correct. When Sharik chooses an answer the computer indicates whether the answer is right or wrong. Sharik first chooses one of the three suggested answers at random. If this answer is wrong, he has a second try, choosing an answer at random from the remaining 2. If this answer is also wrong, Sharik then chooses the remaining answer, which must be correct.
Draw a fully labelled tree diagram to illustrate the various choices that Sharik can make until the computer indicates that he has answered the question correctly.
Solution
The tree diagram is constructed as follows:
First choice: Sharik has a probability of \(\frac{1}{3}\) of choosing the correct answer (C) and \(\frac{2}{3}\) of choosing a wrong answer (W).
Second choice (if first was wrong): From the remaining two answers, the probability of choosing the correct answer is \(\frac{1}{2}\) and the wrong answer is \(\frac{1}{2}\).
Third choice (if second was also wrong): The remaining answer must be correct, so the probability is 1.
The tree diagram shows these probabilities and the paths leading to the correct answer.