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Probability, Applied Statistics

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2.1 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 2.1 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. Supply a probability tree with your solution.
actually open. Supply a probability tree with your solution.

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