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Suppose a certain traffic light shows a red light for 50 seconds, a green light for 50 seconds, and a yellow light for 5 seconds. If you look at this light at some randomly selected instant, what is the probability you will see a yellow or green light?

Respuesta :

MrRoyal

Answer:

[tex]P(Yellow\ or\ Green) = 0.524[/tex]

Step-by-step explanation:

Given

[tex]Yellow = 5\ seconds[/tex]

[tex]Green = 50\ seconds[/tex]

[tex]Red = 50\ seconds[/tex]

Required

Determine the probability of Green or Yellow

First, we need to determine the total time

[tex]Total = 50 + 50 + 5[/tex]

[tex]Total = 105\ seconds[/tex]

Next, is to determine the required probability

This is calculated as follows:

[tex]P(Yellow\ or\ Green) = P(Yellow) + P(Green)[/tex]

[tex]P(Yellow\ or\ Green) = \frac{n(Yellow)}{Total} + \frac{n(Green)}{Total}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{5}{105} + \frac{50}{105}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{5 + 50}{105}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{55}{105}[/tex]

[tex]P(Yellow\ or\ Green) = 0.52380952381[/tex]

[tex]P(Yellow\ or\ Green) = 0.524[/tex] -- Approximated