Contingency Tables · Example 1

Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data:
$$\begin{array}{cccc}& \text{Speeding violation in the last year}& \text{No speeding violation in the last year}& \text{Total}\\ \text{Uses cell phone while driving}& \text{25}& \text{280}& \text{305}\\ \text{Does not use cell phone while driving}& \text{45}& \text{405}& \text{450}\\ \text{Total}& \text{70}& \text{685}& \text{755}\end{array}$$

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755.
Calculate the following probabilities using the table.

a. Find P(Driver is a cell phone user).
b. Find P(driver had no violation in the last year).
c. Find P(Driver had no violation in the last year AND was a cell phone user).
d. Find P(Driver is a cell phone user OR driver had no violation in the last year).
e. Find P(Driver is a cell phone user GIVEN driver had a violation in the last year).
f. Find P(Driver had no violation last year GIVEN driver was not a cell phone user)

OpenStax, Introductory Statistics 2e · §3.4 Contingency Tables · Example 1