I have a bunch of questions to work on with this specific scenario but I was hoping someone can just help me get started on the first one because I'm having trouble getting started and I'll do the rest on my own.Thanks for any help!

In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station,
a. what is the probability that none will pass inspection?

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

.05^10 = ?

To find the probability that none of the next ten automobiles will pass inspection, we can use the concept of independent events. Since each automobile's inspection result is independent of others, we can use the probability of a single automobile not passing inspection to calculate the probability for all ten.

Given that 5% of all automobiles in the state do not pass inspection, the probability of a single automobile not passing inspection is 0.05 (or 5%). To find the probability that none of the next ten automobiles will pass inspection, we multiply this probability by itself ten times.

So, the calculation is:

P(none passing inspection) = P(not passing inspection) × P(not passing inspection) × P(not passing inspection) × ... (ten times)

P(none passing inspection) = 0.05 × 0.05 × 0.05 × ... (ten times)

To simplify this calculation, we can raise the probability of not passing inspection (0.05) to the power of ten:

P(none passing inspection) = 0.05^10

Calculating this, we find:

P(none passing inspection) ≈ 0.0000000001

Therefore, the probability that none of the next ten automobiles will pass inspection is approximately 0.0000000001, or 1 in 10 billion.