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 0.886
(round to three decimal places as needed.)
(b) determine the probability that a randomly selected fatal crash in 2020 occurred in daylight
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 drivers

Sum all values in the contingency table.
$$10646 + 5303+6661 + 970+1041+782+806+112+146+38+96+16$$
$$=(10646+5303)+(6661 + 970)+(1041+782)+(806+112)+(146+38)+(96+16)$$
$$=15949+7631+1823+918+184+112$$
$$=(15949+7631)+(1823+918)+(184+112)$$
$$=23580+2741+296$$
$$=23580+(2741 + 296)$$
$$=23580+3037$$
$$=26617$$

Step2: Calculate number of drivers in daylight

Sum the values in the 'Daylight' column.
$$10646+1041 + 146=11833$$

Step3: Calculate probability

Probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So \(P=\frac{11833}{26617}\approx0.445\)

Answer:

\(0.445\)