probability, Advanced Statistics

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Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the door can be opened; a yellow light indicates that the door is locked from the inside. Suppose that 90% of the time when the card is inserted, the door should open and a green light will appear with probability 0.98. When the door should not open a green light may still appear (electronic error) 5% of the time. Suppose a card has just been inserted and the light is green.
What is the probability that the door will actually open

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