Inspired by Nihar and Sandeep

Probability Level 2

When a non-negative integer $x$ is divided by 5, we get a remainder $y$ such that the number $x$ can be represented as $x=q×5+y$ . For an explicit example if $x=41$ , then we have $x=8×5+1$ . And note that the remainder, here, is 1.

If I give you three chances to enter the integer $y$ , what is the probability that you will get the question right on the third attempt?

Clarification:

You will have to come up with a valid option (a possible remainder which we get after division by 5) each time you enter an integer.
The remainder is defined being bounded in the interval $[0, 5)$

it is impossible to get the question correct.

\frac{1}{5}

\frac{3}{5}

1 solution

Abhay Tiwari
Apr 23, 2016

To get the question right in the third attempt, the first two attempts should be wrong.

Therefore Probability to get correct answer in third attempt let's call it $P(a)$

$P(a)=\frac{4}{5}×\frac{3}{4}×\frac{1}{3}=\frac{1}{5}$

But, you wouldn't be ignorant enough to put in the same answer 3 times! Brilliant wouldn't let you! Thus, the answer is $\frac{1}{3}$ .

Furthermore, you have not specified whether the remainder is non-negative and bounded between 0 and $x$ . We can also have answer as 'It is impossible to get the question correct.'

Sharky Kesa - 5 years, 1 month ago

Please read the question carefully, I have mentioned that the question will get correct in the third attempt.

Abhay Tiwari - 5 years, 1 month ago

Oh, I see my error! My second statement is still valid.

Sharky Kesa - 5 years, 1 month ago

@Sharky Kesa – Sharky, I have edited the problem on the basis of your second statement, though it was correct before also but introducing the word $non-negative$ make sense in the question. Thanks a lot. And for your other doubts I have replied in the report section, please check it.

Abhay Tiwari - 5 years, 1 month ago

I also think the answer is 1/3

Prabalpreet Singh - 5 years, 1 month ago

Shouldnt it be 3/4 x 2/3 x 1/2? When x is divided by 5, the remainders can either be 1,2,3 or 4. Therefore the number of outcomes is 4, not 5.

Ray Baeck - 5 years, 1 month ago

Since we are not known of the number $x$ , there is a possibility that the number might be a multiple of 5 and thus the remainder can also be 0, and that's why it will also be included

Abhay Tiwari - 5 years, 1 month ago

Inspired by Nihar and Sandeep

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