Question

# Papu takes a test and he is very 'determined' about passing the test. He will not give up until he passes the test. How would the sample space of results look like if p stands for pass and F stands for fail, given that he can take the test atmost five times and no test after passing?

A

{{P}, {FP}, {F, F, P}, {F, F, F, P}, {F, F,F, F, P}}

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B

{{F}, {PF}, {P, P, F}, {P, P,P, F}}

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C

{{P}, {FP}, {F, F, P}, {F, F, F, P}, {F,F,F,F, P} {F,F,F,F,F}}

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D

None of these

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Solution

## The correct option is B {{P}, {FP}, {F, F, P}, {F, F, F, P}, {F,F,F,F, P} {F,F,F,F,F}} There are five tests and Papu will take the test again if he does not pass, until the number of attempts is five. Suppose he gets p in the first attempt, then he won't take any more tests. So the outcome will be {P} If he fails in the first one, then the chances are he will pass or fail in the second one. If he passes, the outcome will be {F, P}. If he fails again, we have to look for the third result. If we continue like this, the outcomes we are going to get are {F,F,P}, {F,F,F,P}, {F,F,F, F, P}, and {F,F,F, F, F,} Combining this with initial two outcomes, we get option C.

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