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