Consider this scenario: a traffic signal for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. the traffic policemen want to know the probability that out of the next x number of eastbound cars that arrive at that signal(where x> 3), 3 of them would be stopped by a red light. what is the probability that out of the next 8 eastbound cars that arrive at the signal, exactly 3 will be stopped by a red light? 0.254 0.552 0.806 0.448

0.254

Step-by-step explanation:

Given : A traffic signal for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds.

To Find: What is the probability that out of the next 8 eastbound cars that arrive at the signal, exactly 3 will be stopped by a red light?

Solution:

A traffic signal for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds.

Total time = 15+5+30=50

So, probability of occurring red light =

So, Probability of not occurring red light =

Now we are supposed to find  the probability that out of the next 8 eastbound cars that arrive at the signal, exactly 3 will be stopped by a red light

So, we will use binomial

Substitute n = 8

r = 3

p is the probability of success that is probability of occurring red light = 0.3

q is the probability of failure that is probability of not occurring red light=0.7

So,

Thus the probability that out of the next 8 eastbound cars that arrive at the signal, exactly 3 will be stopped by a red light is 0.254

Hence Option A is true.