Question

23.
a group of 125 pick - up truck owners were asked what brand truck they own and whether it has 4 - wheel drive. the results are given in the two - way table below.
suppose one pick - up truck owner from this group is selected randomly.

a. what is the probability of \yes\, given the brand is a ford?

b. what is the probability a randomly selected truck owner drives a chevy or is a
o\?

Explanation:

Step1: Define conditional probability

For part (a), use conditional probability formula: $P(\text{Yes}|\text{Ford}) = \frac{P(\text{Yes and Ford})}{P(\text{Ford})}$

Step2: Substitute values from table

$P(\text{Yes and Ford}) = \frac{28}{125}$, $P(\text{Ford}) = \frac{45}{125}$
$P(\text{Yes}|\text{Ford}) = \frac{\frac{28}{125}}{\frac{45}{125}} = \frac{28}{45}$

Step3: Define "or" probability for part (b)

Use addition rule: $P(\text{Chevy or No}) = P(\text{Chevy}) + P(\text{No}) - P(\text{Chevy and No})$

Step4: Substitute values from table

$P(\text{Chevy}) = \frac{50}{125}$, $P(\text{No}) = \frac{45}{125}$, $P(\text{Chevy and No}) = \frac{18}{125}$
$P(\text{Chevy or No}) = \frac{50}{125} + \frac{45}{125} - \frac{18}{125} = \frac{77}{125}$

Answer:

a. $\frac{28}{45}$
b. $\frac{77}{125}$