Solve the problem.
-A traffic light at an intersection has a 120-sec cycle. The light is green for 80 sec, yellow for 5 sec, and red for 35 sec.
a. When a motorist approaches the intersection, find the probability that the light will be red.
(Assume that the color of the light is defined as the color when the car is 100 ft from the Intersection. This is the approximate distance at which the driver makes a decision to stop or go.)
b. If a motorist approaches the intersection twice during the day, find the probability that the light
Will be red both times.
A) a. $\frac { 7 } { 24 }$; b. $\frac { 7 } { 48 }$
B) a. $\frac { 7 } { 24 } ;$ b. $\frac { 49 } { 576 }$
C) a. $\frac { 1 } { 3 } ;$ b. $\frac { 1 } { 9 }$
D) a. $\frac { 1 } { 3 }$; b. $\frac { 1 } { 6 }$

Question

Solve the problem.
-A traffic light at an intersection has a 120-sec cycle. The light is green for 80 sec, yellow for 5 sec, and red for 35 sec.
a. When a motorist approaches the intersection, find the probability that the light will be red.
(Assume that the color of the light is defined as the color when the car is 100 ft from the Intersection. This is the approximate distance at which the driver makes a decision to stop or go.)
b. If a motorist approaches the intersection twice during the day, find the probability that the light
Will be red both times. 
A) a. $\frac { 7 } { 24 }$; b. $\frac { 7 } { 48 }$
B) a. $\frac { 7 } { 24 } ;$ b. $\frac { 49 } { 576 }$
C) a. $\frac { 1 } { 3 } ;$ b. $\frac { 1 } { 9 }$
D) a. $\frac { 1 } { 3 }$; b. $\frac { 1 } { 6 }$

Quizplus · Accepted Answer

a. The probability that the light will be red is the duration of the red light divided by the total cycle time, which is $ \frac{35}{120} = \frac{7}{24} $. b. The probability that the light will be red both times a motorist approaches the intersection is the product of the probabilities for each approach, which is $ \left(\frac{7}{24}\right)^2 = \frac{49}{576} $.

Solve the Problem 724\frac { 7 } { 24 }247​ ; B

Solve the Problem $\frac { 7 } { 24 }$ ; B