Statistics

Problem Statement for "PrimeSoccer"

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

  1. 50

    50

    Returns: 0.5265618908306351

  2. 100

    100

    Returns: 0.0

    Both teams will score a goal in each interval, so the final result will be 18 to 18.

  3. 12

    89

    Returns: 0.6772047168840167

  4. 43

    12

    Returns: 0.6967817545210753

  5. 55

    100

    Returns: 0.32120857144574655

  6. 0

    50

    Returns: 0.3119316101074219

  7. 0

    0

    Returns: 0.0

  8. 1

    1

    Returns: 0.02727121816404319

  9. 1

    100

    Returns: 0.01372986366008384

  10. 99

    1

    Returns: 0.1633771511659839

  11. 78

    11

    Returns: 0.6480645387523168

  12. 17

    17

    Returns: 0.8352494291961116

  13. 18

    19

    Returns: 0.8345272105589906

  14. 17

    23

    Returns: 0.8240750197973934

  15. 17

    83

    Returns: 0.6970466307894632

  16. 78

    12

    Returns: 0.6676645940835624

  17. 19

    19

    Returns: 0.8336063890380028

  18. 20

    20

    Returns: 0.8300960715969234

  19. 83

    83

    Returns: 0.44291092001576443

  20. 76

    89

    Returns: 0.5172470324584015

  21. 42

    94

    Returns: 0.6011829426223376

  22. 1

    9

    Returns: 0.4417697199997768

  23. 8

    7

    Returns: 0.5923754549464548

  24. 3

    5

    Returns: 0.2942561210017241

  25. 19

    21

    Returns: 0.8294554174803039

  26. 99

    99

    Returns: 0.28043890109834946

  27. 33

    44

    Returns: 0.6427002434550181

  28. 78

    43

    Returns: 0.5330449279924205

  29. 43

    76

    Returns: 0.546525257727783

  30. 38

    72

    Returns: 0.6058808825290922

  31. 42

    44

    Returns: 0.5746012495371897

  32. 12

    26

    Returns: 0.7854068947455727

  33. 19

    29

    Returns: 0.7984336328904318

  34. 74

    47

    Returns: 0.5415780571348757

  35. 24

    25

    Returns: 0.8000888645683668

  36. 1

    99

    Returns: 0.1633771511659839

  37. 18

    80

    Returns: 0.7026232773993955

  38. 34

    46

    Returns: 0.6272304912663792

  39. 53

    87

    Returns: 0.5034477777634486

  40. 28

    32

    Returns: 0.7446137516111067

  41. 23

    12

    Returns: 0.7986542487841684

  42. 20

    40

    Returns: 0.7432251317619454

  43. 13

    87

    Returns: 0.6790280442414693

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