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 0.445
(round to three decimal places as needed)
(c) determine the probability that a randomly selected fatal crash in 2020 occurred in normal weather and in daylight
the probability is 0.400
(round to three decimal places as needed)
(d) determine the probability that a randomly selected fatal crash in 2020 occurred in normal weather or in daylight
the probability is
(round to three decimal places as needed)
contingency table
light condition
dark, but
weather daylight 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: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a crash occurred in normal weather and \(B\) be the event that a crash occurred in daylight.

Step2: Identify \(P(A)\), \(P(B)\) and \(P(A\cap B)\)

From the problem:

• \(P(A) = 0.886\) (probability of normal - weather crash)
• \(P(B)=0.445\) (probability of daylight crash)
• \(P(A\cap B) = 0.400\) (probability of normal - weather and daylight crash)

Step3: Calculate \(P(A\cup B)\)

Substitute the values into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(0.931\)