## Amazon Interview Question

SDE-2s**Country:**United States

**Interview Type:**In-Person

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Thinking out loud her - answer is not complete.

- Sunny August 31, 2017The remaining runs to win is T_b - T_a. It has to be achieved in 120 - B_b where B_b is the number of balls faced by Team B till now.

Now each ball has a possibility in the set { 0, 1, 2 ,3, 4, 5, 6, NoBall, Wide, Wicket }

The possibilities which contribute to runs are {1,2,3,4,5,6,Wide,NoBall}

There are 120 - B_b balls remaining lets say it is "b" for simplicity.

For each ball there are 10 possibilities and hence b*10 total possiblitites to pick from

But scoring possiblities are 8. hence b*8 possibilities

Probability of picking these possibities are b*8/b*10 = 4/5.

Its not over yet.

lets say target is T = T_a - T_b + 1

then T can be expressed as linear expression of those 8 possibilities.

let us say each coefficient in that linear expression is a_1, a_2, a_3, ....a_8.

Now lets say there are "n" such linear expressions

Out of those "n" such linear expressions only some are valid

--> when the sum of coefficients a_1 to a_8 is b

Lets say this number is "m".

If n == 0 then probability is 0

else if m == 0 then probability is 0

else

total probability is (4/5)*(m/n)