SDE - Intern

You have been given two integers 'N' and 'D', Your task is to find the square root of the number 'N' with precision up to 'D' decimal places i.e. the difference between your answer and the correct answer should be less than 10 ^ (-D).
For example if N = 10 and D = 3, then your answer will be 3.162.

Collision doesn’t happen only in following two cases
1) All ants move in counterclockwise direction.
2) All ants move in clockwise direction.

Since every ant has two choices (pick either of two edges going through the corner on which ant is initially sitting), there are total 23 possibilities.
Out of 23 possibilities, only 2 don’t cause collision. So, the probability of collision is 6/8 and the probability of non-collision is 2/8.

Ask any guard “What would the other guard say if I ask which way is to the hell ?”
And whatever answer he give is the way to the heaven.
Explaintation:
If you end up asking the question to the truthful one, he will speak the truth and he knows that other guard is going to lie so he will show the way to the heaven.
If you end up asking the question to the liar, he will lie about the other and the answer will be the way to the heaven.

Let P(R) be the probability of picking a red marble.

P(R) = P(B1) * P(B1 | J1) + P(B2) * P(B2 | J2)

Here, P(B1) and P(B2) refers to selecting B1 and B2 and the probability of selecting each box is \frac{1}{2} J1 and J2 refers to number of total balls in B1 and B2 respectively.



If we do not reshuffle any balls. Then

P(R) = ((1 / 2) * 1) + ((1 / 2) * 0) = 0.5

But, If we decrease the number of red balls in box B1 and increase the number of red balls in box B2 then the probability of getting a red ball will be maximized.
Therefore, let us take 49 red marbles from B1 to B2 then there will be 1 red ball in B1 and 99 balls in B2 out of which 49 are red and 50 of them are blue in the second jar.
Then

P (R) = ((1 / 2) * (1 / 1)) + ((1 / 2) * (49 / 99)) = 0.747474

Hence,

the maximum probability of choosing a red ball is 0.747474