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The number of passengers on the trip was $76$

The number of passengers in first-class is $12$people.

$64$The number of people in the coach class is 64.

$n=10$travelers were chosen for screening. We'll need to create a simulation to assess if this outcome is likely to occur by chance.

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$ (happens frequently) (always occurs).

Looking at the question, the following is the question of interest expressed in probability language: What are the chances that a random screening of $10$ passengers includes none from first class out of $12$ first class passengers and $64$ coach class passengers? This is the question expressed in probabilistic terms.

To simulate one repetition of the procedure using random digits, we shall perform as follows: As we know, numbers $01-12$can represent first class passengers while $13-76$can represent coach class people. Then, from a line of the random digits table, ten two-digit numbers could be selected, skipping repeated numbers and those from $77to100$The number of first-class passengers in the group may then be counted. The number of first-class passengers is hence the variable being measured.

As in the question, the random digits are as follows: Choose the first two digits of the number. If the number is between$01$and $76$, select the appropriate passenger; otherwise, disregard the number and proceed to the next two-digit number. This is explained as follows:

$71→$Select passenger$71$

$48→$Select passenger$48$

$70$⇒ Select passenger$70$

$99$⇒ Ignore

84$→$Ignore

29$→$Select passenger$29$

$07$⇒ Select passenger$07$

$71$⇒ Repeated thus ignore

$48$⇒ Repeated thus ignore

$63$⇒ Select passenger$63$

$61$⇒ Select passenger$61$

$68$⇒ Select passenger$68$

$34$⇒ Select passenger$34$

$70$⇒ Repeated thus ignore

$52$⇒ Select passenger$52$

Thus the numbers selected are as: $71,48,70,29,07,63,61,68,34,52$.

Numbers $01-12$might represent first-class passengers, whereas $13-46$ could represent coach-class passengers, as we know. The first class passengers might then be measured by taking ten two-digit numbers from a line of the random digits database, skipping over repeated numbers and those from $77-100$ When the exercise was repeated $100$ times, none of the ten passengers picked were sat in first class $15$ times. This could mean that the ten passengers chosen have a number between $13$ and $76$, which reflects coach class passengers, or a number between $77$ and $100$, which indicates that they are skipped. This can happen if ten numbers are chosen at random.