Question

the following data represent a sample of the number of drivers involved in a fatal crash in 2020 in various light and weather conditions. complete parts (a) through (e)
click the icon to view the contingency table
(a) determine the probability that a randomly selected fatal crash in 2020 occurred in normal weather
the probability is
(round to three decimal places as needed.)
contingency table
light condition
weather daylight dark, but lighted dark dawn/dusk
normal 10,646 5,303 6,661 970
rain 1,041 782 806 112
snow/sleet 146 38 96 16

Explanation:

Step1: Calculate total number of fatal crashes

Add all the values in the contingency table.

$$\begin{align*} &\text{Total}=10646 + 5303+6661 + 970+1041+782+806+112+146+38+96+16\\ &=10646+5303 = 15949;15949+6661=22610;22610 + 970=23580;\\ &23580+1041 = 24621;24621+782=25403;25403+806=26209;\\ &26209+112=26321;26321+146=26467;26467+38=26505;\\ &26505+96=26601;26601+16=26617 \end{align*}$$

Step2: Calculate number of crashes in normal weather

Add the values in the "Normal" row.
$$10646+5303 + 6661+970=(10646+5303)+(6661 + 970)=15949+7631 = 23580$$

Step3: Calculate the probability

Probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, favorable outcomes (normal - weather crashes) \(n = 23580\), total outcomes \(N=26617\). So \(P=\frac{23580}{26617}\approx0.886\)

Answer:

\(0.886\)