Python Practice 15/22

Probability calculator

Simulating randomness usually means import random - but that makes a lesson impossible to grade with an exact ==, since the "right" answer changes every run. The fix: a linear congruential generator (LCG), a tiny formula that produces a deterministic stream of numbers that look random but are 100% reproducible from a fixed seed. Same seed in, same numbers out, every single time.

You're given the generator already written - it's not something you need to implement:

def lcg(seed):
    state = seed
    while True:
        state = (state * 1103515245 + 12345) % (2**31)
        yield state / (2**31)

lcg(seed) is a generator (phase 7): calling next() on it gives you the next float in [0, 1). To use one of those floats to pick an item from bag (a list of color-name strings, with duplicates - e.g. ['red']*5 + ['blue']*3 for a bag weighted 5-to-3 toward red), scale it into a valid index: bag[int(r * len(bag))].

Your task: write simulate_draws(bag, n, seed). Create one generator with lcg(seed), then draw from bag with replacement n times - each draw pulls the next float from the generator and uses it to pick one item from bag as described above. Return a dict mapping each color that was drawn to how many times it came up.

You'll practice:

Driving a generator with next() to get a reproducible sequence of values
Turning a [0, 1) float into a valid list index
Building up a count dict across n iterations

def lcg(seed):
    state = seed
    while True:
        state = (state * 1103515245 + 12345) % (2**31)
        yield state / (2**31)

# Write simulate_draws(bag, n, seed): draw from bag WITH replacement n times,
# using lcg(seed) for randomness - next(gen) gives r in [0, 1), and
# bag[int(r * len(bag))] picks one item. Return {color: count}.
def simulate_draws(bag, n, seed):
    pass