Answer:
0.56 is the required probability.
Step-by-step explanation:
Time for which signal shows green light = 4 minutes
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes
To find:
Probability that the signal will show green light when you reach the destination = ?
Solution:
First of all, let us convert each time to same unit before doing any calculations.
Time for which signal shows green light = 4 minutes = 4 [tex]\times[/tex] 60 seconds = 240 seconds
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes = 3 [tex]\times[/tex] 60 seconds = 180 seconds
Now, let us have a look at the formula for probability of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, E is the event that green light is shown by the signal.
Number of favorable cases mean the time for which green light is shown and Total number of cases is the total time (Time for which green light is shown + Time for which Yellow light is shown + Time for which red light is shown)
So, the required probability is:
[tex]P(E) = \dfrac{240}{240+10+180}\\\Rightarrow P(E) = \dfrac{240}{430}\\\Rightarrow \bold{P(E) \approx 0.56 }[/tex]
