Due to the high incidence of crime, a company is giving its employees new and se

Question

Due to the high incidence of crime, a company is giving its employees new and secured access to thecompany. Instead of leaving the doors open, they are installing a card system. To open the door employeesmust insert a cad into a slot.If a green light comes onit is okay to turn the handle and open the door if a yellow light comes on it indicates the door is locked from inside and you cannot enter. Suppose that 90% of the time when the card is inserted the door should be open because it is not locked from inside. when the door should open the system makes errors 2% of the time. That is the green light would appear 98% of the time. when the door should not open the system makes errors 5% of the time green light appears.Suppose you inserted the card and the light is green, what is the probability the door will open?

Explanation / Answer

Ans:

Given that

P(green/door should open)=0.98

P(yellow/door should open)=0.02

P(green/door should not open)=0.05

P(yellow/door should not open)=0.95

P(door should open)=0.9

Now find:

P(green)=P(green/door should open)*P(door should open)+P(green/door should not open)*P(door should not open)

=0.98*0.9+0.05*0.1=0.887

We have to find:

P(door should open/green)=P(green/door should open)*P(door should open)/P(green)

=0.98*0.9/0.887=0.9944

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