Fair Play or Not?
In a game show, a contestant is asked to choose one of three doors, behind one of which is a car. The host then opens one of the other two doors, revealing a goat behind it. Assuming that the contestant switches doors, what is the probability that the car is behind their initial choice versus the door they switch to?
1 Answer
📌 CONCEPT: The probability of winning a car in a game show is analyzed by comparing the contestant's initial choice with the door they switch to, assuming one of the two doors has a goat behind it.
📐 RULE / FORMULA: The probability of the car being behind the initial choice is 1/3, and the probability of the car being behind the switched door is 2/3.
💡 WORKED EXAMPLE: Suppose there are three doors, A, B, and C. The car is initially behind door C. The contestant chooses door A and then switches to door B. The probability of the car being behind door A is 1/3, and the probability of the car being behind door B is 2/3.
⚠️ COMMON MISTAKE: Students often assume the probability remains 1/2 for both doors after the host opens one, forgetting that the contestant's initial choice is a random event with a 1/3 chance of being correct.
09 Jun 26
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