# Traffic light probability question.Need help!!

##### New Member
Hi,
Need help to solve this probability question.

At a certain traffic signal red for 30 seconds, yellow for 5 seconds, and green for 25 seconds. Find the probability that out of the next ten cars that arrive randomly at the light, exactly four will be stopped by a red light.
a. 0.2
b. 0.38
c. 0.625
d. 0.5

##### New Member
Hi,
Need help to solve this probability question.

At a certain traffic signal red for 30 seconds, yellow for 5 seconds, and green for 25 seconds. Find the probability that out of the next ten cars that arrive randomly at the light, exactly four will be stopped by a red light.
a. 0.2
b. 0.38
c. 0.625
d. 0.5o

1 min= 60seconds

red signal = 30 sec. 30/60= 0,5000
yellow signal = 5 sec. 5/60= 0,0833
green signal = 25 sec. 25/60= 0,4167

10 cars = 100% or 1
4 cars = 40% or 0,4 (4/10)

Red signal AND four cars = 0,5x0,4= 0,2 or 20%

#### rogojel

##### TS Contributor
Hi,
You could look at this as a set of 10 trials, as each car tries to pass the light. The probability of being stopped by the red light is 0.5 for each car so, the probability of exactly 4 cars being stopped out of 10 will be C(4,10)*p*(1-p) = 0.205 where C(4,10) is the combination of 4 elements taken from 10 and p is 0.5.

regards
rogojel