# A group of 125 truck owners were asked what brand of truck they owned and whether or not the truck has four-wheel drive. The results are summarized in

Two-way tables
A group of 125 truck owners were asked what brand of truck they owned and whether or not the truck has four-wheel drive. The results are summarized in the two-way table below. Suppose we randomly select one of these truck owners.
$$\begin{array}{c|cc} & \text { Four-wheel drive} & \text { No four-wheel drive } \\\hline \text { Ford } & 28 & 17 \\ \text { Chevy } & 32 & 18 \\ \text { Dodge } & 20 & 10 \end{array}$$
What is the probability that the person owns a Dodge or has four-wheel drive?
$$(a) \frac{20}{80}$$
$$(b) \frac{20}{125}$$
$$(c) \frac{80}{125}$$
$$(d) \frac{90}{125}$$
$$(e) \frac{110}{125}$$

2021-01-11

Given:
$$\begin{array}{c|cc} & \text { Four-wheel drive} & \text { No four-wheel drive } \\\hline \text { Ford } & 28 & 17 \\ \text { Chevy } & 32 & 18 \\ \text { Dodge } & 20 & 10 \end{array}$$
Let us first determine the row/column totals, which is the sum of all counts in the row/column.
$$\begin{array}{c|cc|c} & \text { Four-wheel drive} & \text { No four-wheel drive }&\text{Total} \\\hline \text { Ford } & 28 & 17 &28+17=45 \\ \text { Chevy } & 32 & 18 & 32+18=50\\ \text { Dodge } & 20 & 10 & 20+10=30\\ \hline \text{Total}&28+32+20=80&17+18+10=45& 45+50+30=125 \end{array}$$
The table contains 125 people in total, which is given in the bottom right corner of the table.
The people who own a dodge or have four-wheel drive are given in the row "Dodge” and given in the column ”Four-wheel drive” of the above table, which corresponds with 28+ 32+ 20+ 10= 90 people.
Thus 90 of the 125 people own a dodge or have four-wheel drive.
The probability is the number of favorable outcomes divided by the number of possible outcomes:
$$P(\text{ Dodge or four-wheel drive})=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{90}{125}$$
Answer: (d) $$\frac{90}{125}$$