Question

A review of traffic citations in Dayton found that 40% of drivers cited were issued tickets for speeding, 25% were cited for reckless driving, and 10% were cited for both speeding and reckless driving a. Your roommate got a ticket for speeding. What is the probability that s(he) was also ticketed for reckless driving . b. Based on your answer to part a, what can we say about the relationship between speeding and reckless driving

Answer 1

P( speeding ) = 0.4
P( reckless driving ) = 0.25
P( both ) = 0.10

a) Using bayes theorem, given that the ticket was given for speeding, he was also given for reckless driving is computed as:

P( reckless | speeding ) = P( both ) / P( speeding ) = 0.10 / 0.40 = 0.25

Therefore 0.25 is the required probability here.

b) Based on part a) we see that it the 2 variables are not that highly correlated as the conditional probability is low. We can also computed another measure:
P( speeding | reckless driving ) = P(both ) / P( reckless ) = 0.1 / 0.25 = 0.4

Again the probability is very low, therefore the 2 variables are very unlikely to happen together.