Question

Every day a school bus driver passes the same traffic light twipe, once before school and once after. Each time he passes the light, he records if it is red, green, or yellow. Here is a summary of the data he got after 100 days.

Traffic light before school Traffic light after school Number of days
red red 13
red green 8
red yellow 9
green red 11
green green 7
green yellow 13
yellow red 12
yellow green 15
yellow yellow 12

Suppose the driver will continue recording the colors for 250 more days. In how many of these 250 days will the light be green neither time? Use the data to make a prediction

Answer 1

By calculating the experimental probability from the 100-day observation (46 non-green days out of 100), we predict that approximately 115 out of the next 250 days will have the traffic light be green neither time the school bus passes it.

Step-by-step explanation:

The question involves using experimental probability to predict future events based on historical data. The student is asked to use the provided summary of observations of a traffic light's color at two different times of the day, over 100 days, to predict the number of days the light will be green neither time if observations continue for another 250 days.

To make this prediction, we first need to identify the number of days when the traffic light was not green both times (before and after school) from the data set for the 100-day period. To determine this, we add up the days when the light was red or yellow at both times, resulting in:

• Red/Red: 13 days
• Red/Yellow: 9 days
• Yellow/Red: 12 days
• Yellow/Yellow: 12 days

The total is 13 + 9 + 12 + 12 = 46 days.

The experimental probability that the light is green neither time can be calculated by dividing this total by the number of days (46/100). To predict the number of such days out of the next 250, we can multiply the probability by 250, resulting in 46/100 * 250 = 115. Therefore, based on the experimental probability from the 100-day observation, we predict that on approximately 115 of the next 250 days, the traffic light will be green neither time the school bus driver passes it.