A bag contains \(100 gm\) of rice. Mayank and Akul \(wish\) to get some rice from it. If they take less than \(20\) percent of what it originally contained, the Lord of the Rice kills both of them instantly. If not, then He changes the amount of rice to \(half\) of what it previously contained. Also the lower limit becomes 20 percent of the new content and the same thing continues. Find the probability that they will safely get the food atleast \(n\) times, where \(n\) is \(\left[ \min { (sinx+\frac { 2 }{ sinx } ) } \right] \) for \(sin(x)>0\).

Details and Assumptions

All the \(wishes\) made are random without any prior strategy between the two.

If one doesn't get what he \(wishes\), then also they would have to die. For example if Mayank wishes 80 gm and Akul wishes 40 gm, then one of them won't be ssatisfied and then they would be killed.

For example if they were successful at the first time the bag content would become 50 gm, then 25 gm and so on.

4.\(\left[ . \right] \) denotes greatest integer function

- Each time, Both of us wish for something random between 0 and total content at that time, without any mutual discussion.

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