Probability

Hey, I need help finding the probability of a game.

So you start with three dice and have 5 seconds to guess what one of the dice will land on. At level 25 you lose one dice, at level 50 you lose one dice but the remaining dice becomes 12 sided, at level 75 the 12 sided dice becomes 24 sided , there are 100 total levels

You are given two chances for a mistake before losing the game. What is the probability of passing level 100.

You know you can just post your homework assignments to chat gpt, right?

Low but since this is T&U …

import random def simulate_game(trials=100000): successes = 0 for _ in range(trials): mistakes = 0 for level in range(1, 101): if level <= 24: # Levels 1-24: 3 six-sided dice correct_probability = 1/6 elif level <= 49: # Levels 25-49: 2 six-sided dice correct_probability = 1/6 elif level <= 74: # Levels 50-74: 2 twelve-sided dice correct_probability = 1/12 else: # Levels 75-100: 2 twenty-four sided dice correct_probability = 1/24 # Simulate a guess if random.random() < correct_probability: continue # Correct guess else: mistakes += 1 if mistakes > 2: # More than 2 mistakes break if mistakes <= 2: successes += 1 return successes / trials # Run the simulation probability = simulate_game() print(f"Estimated probability of passing level 100: {probability:.4f}")

1.02×10^-69 in theory. This means zero...no one can win this game.

Cool thanks guys. I tried having ChatGPT do it but it gave up after 10m simulations and I didn't know how to do probability 

Probability is extremely low, essentially zero when rounded to ten decimal places. The very low probabilities at higher levels (especially with the twelve-sided and twenty-four-sided dice) make it almost impossible to pass all 100 levels without making more than two mistakes.