Conditional Probabilityhard
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A specialized game show has three doors. Behind one door is a luxury car, while the other two contain goats. The contestant picks a door. The host, who knows the location of the car, opens one of the other doors to reveal a goat. However, the host is 'lazy' and only opens a goat door 50% of the time when he can; otherwise, he ends the game prematurely. Given that he successfully opened a door and showed a goat, what is the probability that switching your choice wins the car?
A specialized game show has three doors. Behind one door is a luxury car, while the other two contain goats. The contestant picks a door. The host, who knows the location of the car, opens one of the other doors to reveal a goat. However, the host is 'lazy' and only opens a goat door 50% of the time when he can; otherwise, he ends the game prematurely. Given that he successfully opened a door and showed a goat, what is the probability that switching your choice wins the car?