Q:

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

Accepted Solution

A:
P(3 reds out of 8) 
= 8C3 * [15 / (15 + 5 + 30)]^3 * [(5 + 30) / (15 + 5 + 30)]^(8 - 3) 
= 8C3 * 0.3^3 * 0.7^5 
= 0.25412184 
= 25.4% 
=~ 0.3