Conditional Probabilityhard
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A specialized game show uses three opaque jars. One jar contains a diamond, while the other two contain pebbles. A contestant selects a jar. The host, who knows the location of the diamond, opens one of the two jars the contestant did not select to reveal a pebble. If the host is 'mischievous' and only opens a jar 75% of the time when he has the option to do so, and otherwise simply ends the game, what is the probability that the diamond is in the jar the contestant originally selected, given that the host successfully revealed a pebble?
A specialized game show uses three opaque jars. One jar contains a diamond, while the other two contain pebbles. A contestant selects a jar. The host, who knows the location of the diamond, opens one of the two jars the contestant did not select to reveal a pebble. If the host is 'mischievous' and only opens a jar 75% of the time when he has the option to do so, and otherwise simply ends the game, what is the probability that the diamond is in the jar the contestant originally selected, given that the host successfully revealed a pebble?