PrimeSoccer | Topcoder Archive

Problem Statement

You are watching a soccer match, and you wonder what the probability is that at least one of the two teams will score a prime number of goals. The game lasts 90 minutes, and to simplify the analysis, we will split the match into five-minute intervals. The first interval is the first five minutes, the second interval is the next five minutes, and so on. During each interval, there is a skillOfTeamA percent probability that team A will score a goal, and a skillOfTeamB percent probability that teamB will score a goal. Assume that each team will score at most one goal within each interval. Return the probability that at least one team will have a prime number as its final score.

Definition

Class:: PrimeSoccer
Method:: getProbability
Parameters:: int, int
Returns:: double
Method signature:: double getProbability(int skillOfTeamA, int skillOfTeamB)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.
A prime number is a number that has exactly two divisors, 1 and itself. Note that 0 and 1 are not prime.

Constraints

skillOfTeamA will be between 0 and 100, inclusive.
skillOfTeamB will be between 0 and 100, inclusive.

Examples

```
50
```
```
50
```
```
Returns: 0.5265618908306351
```
```
100
```
```
100
```
```
Returns: 0.0
```
Both teams will score a goal in each interval, so the final result will be 18 to 18.
```
12
```
```
89
```
```
Returns: 0.6772047168840167
```

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