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A multiple choice question has 5 available options, only 1 of which is correct. Students are allowed 2 attempts at the answer. A student who does not know the answer decides to guess at random, as follows:

On the first attempt, he guesses at random among the 5 options. If his guess is right, he stops. If his guess is wrong, then on the second attempt he guesses at random from among the 4 remaining options.

a)Find the chance that the student gets the right answer at his first attempt. Solution: 0.2

b)Find the chance that the student has to make two attempts and gets the right answer the second time. Solution 0.2

c)Find the chance that the student gets the right answer. I can΄T understand what this question asking me. Solution 0.2 is wrong!

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up vote 2 down vote accepted

The answers to parts a and b show two different ways the student may find the correct answer. Since they cannot both happen, you add the probabilities for the chance that either one happens. The answer is then $0.4$.

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You can also see this by drawing a probability tree. There is a $1/5$ chance he gets is right first. So there is probability $1/5$ already

There is a $4/5$ chance he gets it wrong the first time. Once that happens, 4 choices remain, so he has a $1/4$ chance after the first trial of blundering on the right answer. So the total probabilty for this branch is $1/5 = 4/5\cdot 1/4$.

Since the two occurrences are disjoint, the probability of getting it right on the first two is $2/5$.

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