Question

select the correct answer. a survey was given to randomly selected employees who drive to work. each employee was asked to report if they had received a speeding ticket on their morning commute to work any time in the last year. the results are in the table. regularly leave for work early or on time regularly leave for work late total speeding ticket 5 56 61 no speeding ticket 81 9 90 total 86 65 151 which conclusion can be made from the data? a. the probability of an employee receiving a speeding ticket given that they regularly leave for work late is the same as the probability of an employee not receiving a speeding ticket given that they regularly leave for work early or on time. b. employees who regularly leave for work late are less likely to receive a speeding ticket than employees who regularly leave for work early or on time. c. regularly leaving for work late and receiving a speeding ticket are independent events. d. the probability of an employee not receiving a speeding ticket given that they regularly leave for work early or on time is less than the probability of an employee not receiving a speeding ticket given that they regularly leave for work late.

Explanation:

Step1: Recall probability formula

Probability \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

Step2: Calculate probabilities for different - cases

Let's calculate the probabilities for employees who regularly leave for work early or on - time and those who regularly leave for work late and their relation to getting a speeding ticket.
For employees who regularly leave for work early or on - time (\(n = 86\)), the number of those who got a speeding ticket is \(5\). So the probability \(P(\text{ticket}|\text{early/on - time})=\frac{5}{86}\)
For employees who regularly leave for work late (\(n = 65\)), the number of those who got a speeding ticket is \(61\). So the probability \(P(\text{ticket}|\text{late})=\frac{61}{65}\)
Since \(\frac{5}{86}\lt\frac{61}{65}\), employees who regularly leave for work late are more likely to receive a speeding ticket than employees who regularly leave for work early or on - time.

Answer:

B. Employees who regularly leave for work late are more likely to receive a speeding ticket than employees who regularly leave for work early or on time.