Question

A certain traffic light is red for 20 seconds, yellow for 4 seconds, and green for 36 seconds. Find that probability that of the next 12 cars that randomly arrive at the light, exactly 4 will be stopped by a red light.

Answer 1

To find the probability that exactly 4 out of the next 12 cars will be stopped by a red light, we can use the binomial probability formula. The probability is approximately 0.0541.

Step-by-step explanation:

To find the probability that exactly 4 out of the next 12 cars will be stopped by a red light, we can use the binomial probability formula.

The probability of each car being stopped by a red light is 20/60 (since the red light is on for 20 seconds out of the total cycle time of 60 seconds).

The formula for calculating the binomial probability is: P(x=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success, and C(n,k) is the combination formula.

In this case, n=12, k=4, and p=20/60.

Plugging these values into the formula, we get: P(x=4) = C(12,4) * (20/60)^4 * (1-20/60)^(12-4)

Simplifying the equation gives: P(x=4) = 0.0541 (approximately).