Question

chapter 3: 3.3 two basic rules of probability homework due for ten 14, 2019 11:59pm answer 1 details no additional details were added for this assignment. chapter 3: 3.3 two basic rules of probability homework score: 7/14 answered: 1/8 question 1 the table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.

driver intoxicated?

pedestrian intoxicated?

yes

no

yes

41

78

no

258

609

if one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated. please enter a decimal to 4 decimal places. probability = submit question

Explanation:

Step1: Identify relevant values

Total number of pedestrian - deaths \(n = 986\).
Number of pedestrians intoxicated \(n_{p - intox}=41 + 258=299\).
Number of non - intoxicated drivers \(n_{d - not - intox}=258+609 = 867\).
Number of pedestrians intoxicated and non - intoxicated drivers \(n_{p - intox\&d - not - intox}=258\).

Step2: Use the addition rule of probability

The addition rule for two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Let \(A\) be the event that the pedestrian was intoxicated and \(B\) be the event that the driver was not intoxicated.
\(P(A)=\frac{n_{p - intox}}{n}=\frac{299}{986}\), \(P(B)=\frac{n_{d - not - intox}}{n}=\frac{867}{986}\), and \(P(A\cap B)=\frac{n_{p - intox\&d - not - intox}}{n}=\frac{258}{986}\).
\(P(A\cup B)=\frac{299 + 867-258}{986}=\frac{908}{986}\approx0.9209\)

Answer:

\(0.9209\)