To find the probability that a randomly selected fatal crash in normal weather occurs when it is dark but lighted, follow these steps:
1. Identify the Total Number of Crashes in Normal Weather Conditions:
You are given the number of fatal crashes in various light conditions under normal weather conditions:
- Daylight: 14,307
- Dark, but lighted: 5,875
- Dark: 8,151
- Dawn/Dusk: 1,183
- Other: 65
Summing these values gives the total number of fatal crashes in normal weather conditions:
[tex]\[
14,307 + 5,875 + 8,151 + 1,183 + 65 = 29,581
\][/tex]
2. Identify the Number of Fatal Crashes in Normal Weather That Are Dark but Lighted:
From the data, the number of fatal crashes that occur when it is dark but lighted is 5,875.
3. Calculate the Probability:
The probability [tex]\( P \)[/tex] of a fatal crash occurring under normal weather conditions when it is dark but lighted is the number of dark but lighted crashes divided by the total number of crashes under normal weather conditions:
[tex]\[
P(\text{Dark, but lighted}) = \frac{\text{Number of dark, but lighted crashes}}{\text{Total number of crashes in normal weather}}
\][/tex]
Substituting in the values, we have:
[tex]\[
P(\text{Dark, but lighted}) = \frac{5,875}{29,581}
\][/tex]
Performing the division gives:
[tex]\[
P(\text{Dark, but lighted}) \approx 0.1986072140901254
\][/tex]
4. Round the Probability to Three Decimal Places:
The probability, rounded to three decimal places, is:
[tex]\[
P(\text{Dark, but lighted}) \approx 0.199
\][/tex]
Therefore, the probability that a randomly selected fatal crash in normal weather occurs when it is dark, but lighted is approximately [tex]\( 0.199 \)[/tex].
