midtermproblem1.py

from dataclasses import dataclass
from typing import Literal
import numpy as np
from statistics import mean

np.random.seed(6420)

GradeType = Literal['A', 'B', '<=C']

@dataclass(frozen=True)
class Observation:
    bull: bool
    grade: GradeType
    car: bool
    lottery: bool
    redington: bool


def simulateObservation() -> Observation:
    bull = np.random.uniform() <= .5
    grade: GradeType = np.random.choice(["A", "B", "<=C"], p=[0.6, 0.3, 0.1])
    if bull:
        if grade == "A":
            car = np.random.uniform() <= .8
        elif grade == "B":
            car = np.random.uniform() <= .5
        else:
            car = np.random.uniform() <= .2
    else:
        if grade == "A":
            car = np.random.uniform() <= .5
        elif grade == "B":
            car = np.random.uniform() <= .3
        else:
            car = np.random.uniform() <= .1
    lottery = np.random.uniform() <= .001
    if lottery:
        redington = np.random.uniform() <= .99
    else:
        if car:
            redington = np.random.uniform() <= .7
        else:
            redington = np.random.uniform() <= .2

    return Observation(bull, grade, car, lottery, redington)

obs: list[Observation] = [simulateObservation() for _ in range(100_000)]
# filter out observations where she is not at redington
obs = [o for o in obs if o.redington]
print(mean(o.car for o in obs))
print(mean(o.lottery for o in obs))
print(mean(o.grade == "B" for o in obs))
print(mean(not o.bull for o in obs))