The copy machine in an office is very unreliable.If it was working yesterday, there is an 80% chance it will work today.If it was not working yesterday, there is a 10% chance it will work today.If it is not working today, what is the probability that it will be working 2 days from now?
A)0.16
B)0.17
C)0.34
D)0.66

Question

Quizplus · Accepted Answer

Given the machine is not working today, it either wasn't working yesterday (with a 10% chance of working tomorrow) or it was working yesterday (with a 20% chance of not working today and thus a 10% chance of working the day after). The probability it wasn't working yesterday and works two days from now is 0.9*0.1 = 0.09. The probability it was working yesterday and works two days from now is 0.8*0.2*0.1 = 0.016. The total probability is 0.09 + 0.016 = 0.106, which rounds to 0.11, not matching any options directly due to a mistake in calculation. Correcting the approach: If it's not working today, the chance it works two days from now is directly from its state today, not dependent on yesterday. If not working today, there's a 10% chance it works tomorrow, and regardless of yesterday, this is the relevant probability for it working two days from now, indicating a mistake in the initial explanation. Correct interpretation should focus on the direct transition probabilities from the state of being not working today to the state two days from now, which seems to have been misunderstood in the provided explanation.

The Copy Machine in an Office Is Very Unreliable