Question

The porch light is an automatic switch that will start turning on at 19.00 - 19.30 or 20.00 - 21.00 at random. The lights will automatically go out at some point in time between 04:00 and 06:00 in the morning. Suppose it is known that tonight the light is on for t hours, the probability that the light is on for 9 < t < 10 hours is ...

Answer 1

• Turning on time be x
• Turning of time be y

If 19:00<=x<=19:30 and 4:00<=y<=6:00

Total time difference

$\\ \sf\longmapsto 6:00-19:30=10:30$

• In order to mange time between 9--10 hours 30 minutes should be deducted in pairs from starting and ending .By which net deduction i e x-y=0

• Total starting options=x=15
• Total ending options=x=15
• Sample space=|S|=15+15=30
• E=1

Probability=

$\\ \sf\longmapsto P(E)=\dfrac{1}{30}$