Answer:
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 = [tex]\frac{15}{50}=0.3[/tex]
So, Probability of not occurring red light = [tex]1-0.3=0.7[/tex]
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
[tex]P(X=r)=^nC_r p^rq^{n-r}[/tex]
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, [tex]P(X=3)=^{8}C_{3} (0.3)^3 (0.7)^{5}[/tex]
[tex]P(X=3)=\frac{8!}{3!(8-3)!}(0.3)^3 (0.7)^{5}[/tex]
[tex]P(X=3)=0.254[/tex]
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.
