Question

Studies have shown that passengers in a vehicle increase

Answer 1

Answer:

{0, 1, 2, 3, 4, 5, 6, 7}

Step-by-step explanation:

We know that the probability is modeled by a function:

f(x) = 0.09*(1.43)^x

Where x represents the number of passengers in addition to the driver.

Here we need to remember some things about probability.

We can not have a negative probability.

In the case of a continuous probability distribution, we must have:

$\int\limits^a_b {f(x)} \, dx = 1$

(this means that the sum of probabilities of all possible outcomes is equal to 1)

And in a discrete case, such that we have N events with probabilities P(1), P(2), ..., P(N)

we must have:

P(1) + P(2) + P(3) + ... + P(N) = 1

So if we use that as our criteria to find the correct domain, then all the options are incorrect.

Here we only can use the context of the problem to find the correct domain.

Then let's ask, what does x represent?

the number of passengers.

Now let's see the options and let's see if these domains can represent a given number of passengers or not.

a) All real numbers.

Well, in the set of all real numbers we have numbers like -123.4213

And that clearly can not be a number of passengers, so we can discard this option.

b) {0, 1, 2, 3, 4, 5, 6, 7}

This seems correct, this can mean that you can have from 0 to 7 passengers. (what happens in the case where you have 8 or more? maybe this model does not work for that many passengers)

c) All positive integers.

This seems to solve the problem of having 8 or more passengers, but in this domain, we do not have the number 0 (we have only positive integers) then the case of having no passengers is not modeled, then there is a problem. (Also, in this case, we could have 100,000,000,000. passengers, or even more, and that does not have a lot of sense)

d) 0 ≤ x  ≤ 7

This is all the real numbers between 0 and 7 (0 and 7 included)

Then in this case we have numbers like 3.14

And you can not have 3.14 passengers in your vehicle (you can have 3 of them, and the remaining 0.14?)

So this domain can be discarded.

Then the only domain that makes sense is the second one,  {0, 1, 2, 3, 4, 5, 6, 7}