You have 13 red cards and 13 blue cards, labeled from 1 to 13. You remove 7 blue cards at random. What is the probability that the card drawn is blue given that the number on the card is 3? Please write a simulation that has the probability as an output.

import random def simulate(n_simulations): count_total_3 = 0 count_blue_3 = 0 for _ in range(n_simulations): # Generate the cards red_cards = [(color, number) for color in ['red'] for number in range(1, 14)] blue_cards = [(color, number) for color in ['blue'] for number in range(1, 14)] # Remove 7 random blue cards removed_blue_cards = random.sample(blue_cards, 7) remaining_blue_cards = [card for card in blue_cards if card not in removed_blue_cards] # Combine remaining cards remaining_cards = red_cards + remaining_blue_cards # Draw a card drawn_card = random.choice(remaining_cards) # Check if the drawn card is labeled 3 if drawn_card[1] == 3: count_total_3 += 1 if drawn_card[0] == 'blue': count_blue_3 += 1 if count_total_3 == 0: return 0 # Avoid division by zero if no 3s were drawn at all # Calculate the conditional probability return count_blue_3 / count_total_3 # Number of simulations n_simulations = 100000 probability = simulate(n_simulations) print(f"Estimated probability that the card is blue given that the number is 3: {probability:.4f}")

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