91Ó°ÊÓ

In the question, it is stated that 17% of the vehicles passing through the tollbooth have out-of-state plates, but we are only interested in the number of vehicles that pass through until two out-of-state plates are observed.

We have,

$$\begin{gathered} 17\%=0.17 \\ =\frac{17}{100} \end{gathered}$$

We'll now choose a row from the table of random numbers. The first two-digit number will be chosen after that. If the digit is between $00$and $16$(inclusive), the vehicle has out-of-state plates; otherwise, the vehicle does not have out-of-state plates.

This process will be repeated until two vehicles with out-of-state plates have been obtained. Then we'll keep track of how many trials are required until two vehicles have out-of-state license plates.

First trial: require three vehicles.
The second trial: required$14$vehicles.
The third trial: required $13$vehicles.

In the question, it is stated that 17% of the vehicles passing through the tollbooth have out-of-state plates, whereas we are interested in the total number of vehicles passing through until two vehicles with out-of-state plates are seen.

We have,

$$\begin{gathered} 17\%=0.17 \\ \frac{17}{100} \end{gathered}$$

Therefore, the given rows from the random digits given in the tables are as:

We'll start with the first trial now.

The first two-digit number will be chosen. The vehicle has out-of-state plates if the digit is between $00$and $16$(inclusive); otherwise, the vehicle does not have out-of-state plates. This process will be repeated until two vehicles with out-of-state plates have been obtained.

$41=$Vehicles do not have out-of-state plates

$05⇒$ Vehicles have out-of-state plates
$09⇒$Vehicles have out-of-state plates

Then we note that we'll need three vehicles until we can get two with out-of-state license plates.

We will now conduct a second trial as follows:

The first two-digit number will be chosen. The vehicle has out-of-state plates if the digit is between $00$and $16$(inclusive); otherwise, the vehicle does not have out-of-state plates. This process will be repeated until two vehicles with out-of-state plates have been obtained.

$20⇒$Vehicles do not have out-of-state plates
$31⇒$ Vehicles do not have out-of-state plates
$06⇒$ Vehicles have out-of-state plates
$44⇒$ Vehicles do not have out-of-state plates
$90⇒$ Vehicles do not have out-of-state plates
$50⇒$ Vehicles do not have out-of-state plates
$59⇒$ Vehicles do not have out-of-state plates
59⇒Vehicles do not have out-of-state plates
$88⇒$Vehicles do not have out-of-state plates
$43⇒$ Vehicles do not have out-of-state plates
$18⇒$ Vehicles do not have out-of-state plates
$80⇒$ Vehicles do not have out-of-state plates
$53⇒$ Vehicles do not have out-of-state plates
$11⇒$Vehicles have out-of-state plates

Then, until we get two vehicles with out-of-state plates, we'll need $14$vehicles.

We will now proceed to the third trial, as follows:

The first two-digit number will be chosen. The vehicle has out-of-state plates if the digit is between $00$and $16$(inclusive); otherwise, the vehicle does not have out-of-state plates. This process will be repeated until two vehicles with out-of-state plates have been obtained.

$58⇒$Vehicles do not have out-of-state plates
44⇒Vehicles do not have out-of-state plates
69⇒Vehicles do not have out-of-state plates
94⇒Vehicles do not have out-of-state plates
86⇒Vehicles do not have out-of-state plates
85⇒Vehicles do not have out-of-state plates
79⇒Vehicles do not have out-of-state plates
67⇒Vehicles do not have out-of-state plates
05⇒Vehicles have out-of-state plates
81⟹Vehicles do not have out-of-state plates
18⇒Vehicles do not have out-of-state plates
45⇒Vehicles do not have out-of-state plates
14⇒ Vehicles have out-of-state plates

Then we note that we'll need $13$vehicles until we get two with out-of-state plates.