{
  "kind": "analytical_binomial_distribution",
  "n": 100,
  "p": 0.5,
  "heads": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19,
    20,
    21,
    22,
    23,
    24,
    25,
    26,
    27,
    28,
    29,
    30,
    31,
    32,
    33,
    34,
    35,
    36,
    37,
    38,
    39,
    40,
    41,
    42,
    43,
    44,
    45,
    46,
    47,
    48,
    49,
    50,
    51,
    52,
    53,
    54,
    55,
    56,
    57,
    58,
    59,
    60,
    61,
    62,
    63,
    64,
    65,
    66,
    67,
    68,
    69,
    70,
    71,
    72,
    73,
    74,
    75,
    76,
    77,
    78,
    79,
    80,
    81,
    82,
    83,
    84,
    85,
    86,
    87,
    88,
    89,
    90,
    91,
    92,
    93,
    94,
    95,
    96,
    97,
    98,
    99,
    100
  ],
  "probability": [
    7.888609052210118e-31,
    7.888609052210118e-29,
    3.9048614808440084e-27,
    1.275588083742376e-25,
    3.093301103075262e-24,
    5.939138117904503e-23,
    9.403635353348797e-22,
    1.2627738903068384e-20,
    1.4679746474816996e-19,
    1.5005963063146263e-18,
    1.3655426387463099e-17,
    1.1172621589742536e-16,
    8.286361012392381e-16,
    5.609228993004073e-15,
    3.4857351599382454e-14,
    1.998488158364594e-13,
    1.0616968341311906e-12,
    5.246031415707059e-12,
    2.4190033750204773e-11,
    1.0439909302719954e-10,
    4.2281632676015815e-10,
    1.6107288638482216e-09,
    5.78398092018225e-09,
    1.9615239642357197e-08,
    6.2932227185896e-08,
    1.9131397064512386e-07,
    5.518672230147804e-07,
    1.5125249815960647e-06,
    3.9433687020183116e-06,
    9.790432639493739e-06,
    2.3170690580135184e-05,
    5.232091421320847e-05,
    0.00011281697127223077,
    0.00023247133474277857,
    0.00045810527728724014,
    0.0008638556657416528,
    0.0015597393964779842,
    0.0026979276047186754,
    0.00447287997624412,
    0.00711073226992655,
    0.010843866711637987,
    0.015869073236543397,
    0.022292269546572867,
    0.030068642644214563,
    0.03895255978909614,
    0.048474296626430755,
    0.05795839814029764,
    0.06659049999098027,
    0.07352701040670738,
    0.07802866410507722,
    0.07958923738717877,
    0.07802866410507722,
    0.07352701040670738,
    0.06659049999098027,
    0.05795839814029764,
    0.048474296626430755,
    0.03895255978909614,
    0.030068642644214563,
    0.022292269546572867,
    0.015869073236543397,
    0.010843866711637987,
    0.00711073226992655,
    0.00447287997624412,
    0.0026979276047186754,
    0.0015597393964779842,
    0.0008638556657416528,
    0.00045810527728724014,
    0.00023247133474277857,
    0.00011281697127223077,
    5.232091421320847e-05,
    2.3170690580135184e-05,
    9.790432639493739e-06,
    3.9433687020183116e-06,
    1.5125249815960647e-06,
    5.518672230147804e-07,
    1.9131397064512386e-07,
    6.2932227185896e-08,
    1.9615239642357197e-08,
    5.78398092018225e-09,
    1.6107288638482216e-09,
    4.2281632676015815e-10,
    1.0439909302719954e-10,
    2.4190033750204773e-11,
    5.246031415707059e-12,
    1.0616968341311906e-12,
    1.998488158364594e-13,
    3.4857351599382454e-14,
    5.609228993004073e-15,
    8.286361012392381e-16,
    1.1172621589742536e-16,
    1.3655426387463099e-17,
    1.5005963063146263e-18,
    1.4679746474816996e-19,
    1.2627738903068384e-20,
    9.403635353348797e-22,
    5.939138117904503e-23,
    3.093301103075262e-24,
    1.275588083742376e-25,
    3.9048614808440084e-27,
    7.888609052210118e-29,
    7.888609052210118e-31
  ],
  "probability_exactly_50": 0.07958923738717877,
  "probability_40_through_60": 0.9647997997822952,
  "all_heads_probability": 7.888609052210118e-31,
  "ways_exactly_50": "100891344545564193334812497256"
}