Amazon Interview Question
SDE-2sCountry: 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)