1. Traffic Intersection Probability

At a certain intersection, the light for eastbound traffic is red for15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to thenearest tenth, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red
light.

2. Originally Posted by magentarita
At a certain intersection, the light for eastbound traffic is red for15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to thenearest tenth, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red
light.
Probability of a car being stopped by a red light is p = 15/50 = 3/10.

Let X be the random variable number of cars stopped by a red light.

X ~ Binomial(n = 8, p = 3/10).

$\Pr(X = 3) = {8 \choose 3} \left(\frac{3}{10}\right)^3 \left(\frac{7}{10}\right)^5 = \, ....$

3. ok

Originally Posted by mr fantastic
Probability of a car being stopped by a red light is p = 15/50 = 3/10.

Let X be the random variable number of cars stopped by a red light.

X ~ Binomial(n = 8, p = 3/10).

$\Pr(X = 3) = {8 \choose 3} \left(\frac{3}{10}\right)^3 \left(\frac{7}{10}\right)^5 = \, ....$
It's great to know that you can solve questions in all these categories.