Monty Hall Game
★Exhibit Content: Conditional probability, Monty Hall problem, mathematical statistics, electromechanical interactive experience ★Interaction: Button selection, random simulation, voice prompt, electromechanical interaction ★Operation: 1. Drop the ball into the ball inlet; the system randomly hides the ball behind one of three doors; 2. Press the corresponding button ①②③ to guess which door the ball is behind; the system automatically lights up an empty door; 3. The device gives a voice prompt asking whether to switch; first, do not switch for 10 consecutive rounds and record the number of wins; then switch for 10 consecutive rounds; compare the winning probabilities of the two choices and summarize the probability rule. ★Exhibit Description: "Three-Door Game" is a classic Monty Hall probability problem desktop science exhibit, belonging to the probability and statistics mathematics exhibition area, and is a recommended exhibit of PopsciCat. The exhibit uses a standard white and blue science operation console; above the tabletop, a vertical blue cabinet contains a three-door light display module and a random ball allocation mechanism; on the tabletop, there are metal selection buttons No. 1/2/3 and an acrylic instruction sign with illustrated explanations; inside the cabinet, a PLC control and voice broadcast module are installed. The device automatically randomly allocates the ball position, simulates the host's door-opening process, and guides visitors to compare in groups the number of wins under the two strategies of "not switching" and "switching", visually verifying the conditional probability conclusion and correcting the public's intuitive cognitive misconception. ★Scientific Principle: Initially, with three doors, the probability that each door hides the ball is 1/3: 1. If the target door is chosen initially (probability 1/3), switching will inevitably fail; 2. If an empty door is chosen initially (probability 2/3), the host will open another empty door; at this time, switching will definitely select the ball. Therefore, the winning probability of not switching is 1/3, and the winning probability of switching increases to 2/3; switching can double the winning probability. Through a large number of repeated trials, the exhibit intuitively presents the logic of conditional probability and corrects the deviation of intuitive judgment.
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- 0.9×0.7×1.2m 0.9×0.7×1.2mDimensions (L×W×H): 0.9×0.7×1.2m Brand: PopsciCat Model: PopsciCat-math-127 1. Materials ①Base: 2mm cold-rolled steel frame, 2.0mm cold-rolled steel enclosure with two-tone baked paint, rounded anti-collision edges ②Tabletop: Kelesi artificial stone, thickness ≥12mm, with flame-retardant and moisture-proof bottom board ③Instruction sign: acrylic UV high-definition printing, printed with operation steps and probability derivation of the three-door problem ④Maintenance cabinet: 2.0mm cold-rolled steel with lockable access door for easy maintenance of wiring and electrical control modules ⑤Vertical cabinet: ABS one-piece blue cabinet, embedded with transparent backlit three-door display window ⑥Lighting components: low-voltage soft backlight indicators to distinguish empty doors from winning doors 2. Main Configuration ①Electrical control system: electrical logic control system, equipped with Inertia® K1 PLC controller with protection specially for science exhibits, built-in random allocation and statistical counting programs ②Wuhan Jiajian Chengchu customized three-door backlit light display module ③Voice broadcast prompt module 3. Exhibition Requirements ①Power requirement: AC100-240V, 50/60Hz/100W (standard three-wire grounded socket, supplying power to electrical control, lighting, and voice modules) ②Installation foundation: operation console placed directly on the floor ③Entry passage: door frame dimensions (W×H) ≥1.4m×1.4m, continuous turning interval in passage ≥1.8m ④Maintenance access: not required
★Exhibit Content: Conditional probability, Monty Hall problem, mathematical statistics, electromechanical interactive experience ★Interaction: Button selection, random simulation, voice prompt, electromechanical interaction ★Operation: 1. Drop the ball into the ball inlet; the system randomly hides the ball behind one of three doors; 2. Press the corresponding button ①②③ to guess which door the ball is behind; the system automatically lights up an empty door; 3. The device gives a voice prompt asking whether to switch; first, do not switch for 10 consecutive rounds and record the number of wins; then switch for 10 consecutive rounds; compare the winning probabilities of the two choices and summarize the probability rule. ★Exhibit Description: "Three-Door Game" is a classic Monty Hall probability problem desktop science exhibit, belonging to the probability and statistics mathematics exhibition area, and is a recommended exhibit of PopsciCat. The exhibit uses a standard white and blue science operation console; above the tabletop, a vertical blue cabinet contains a three-door light display module and a random ball allocation mechanism; on the tabletop, there are metal selection buttons No. 1/2/3 and an acrylic instruction sign with illustrated explanations; inside the cabinet, a PLC control and voice broadcast module are installed. The device automatically randomly allocates the ball position, simulates the host's door-opening process, and guides visitors to compare in groups the number of wins under the two strategies of "not switching" and "switching", visually verifying the conditional probability conclusion and correcting the public's intuitive cognitive misconception. ★Scientific Principle: Initially, with three doors, the probability that each door hides the ball is 1/3: 1. If the target door is chosen initially (probability 1/3), switching will inevitably fail; 2. If an empty door is chosen initially (probability 2/3), the host will open another empty door; at this time, switching will definitely select the ball. Therefore, the winning probability of not switching is 1/3, and the winning probability of switching increases to 2/3; switching can double the winning probability. Through a large number of repeated trials, the exhibit intuitively presents the logic of conditional probability and corrects the deviation of intuitive judgment.
Review
Principle Display: ★★★★ Interaction Effect: ★★★★ Ease of Installation: ★★★★★ Durability: ★★★★ Overall Rating: ★★★★