Question

6. A stoplight at an intersection stays red for 60 second, changes to green for 45

Answer 1

Answer:

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds

Step-by-step explanation:

At each second, the stoplight is equally likely to change, which means that we use the uniform probability distribution to solve this question.

Uniform probability distribution:

Has two bounds, a and b. The probability of finding a value higher than x is given by:

$P(X > x) = \frac{b - x}{b - a}$

Red for 60 seconds

So when Jamal arrives it can change in any number of seconds between 0 and 60, that is, $a = 0, b = 60$

Probability that he will have to wait at a red light for more than 15 seconds?

$P(X > 15) = \frac{60 - 15}{60 - 0} = \frac{45}{60} = \frac{3}{4} = 0.75$

0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds