A manager randomly selects one applicant for the job and does not consider them again for another position. Then another applicant is chosen for a different role. Are these selections independent or dependent? Explain your reasoning.

A recent study found that $2.5\%$ of all newborns in a country were delivered by cesarean section due to medical emergencies. Among these emergency cesarean deliveries, $18.7\%$ involved premature births. What is the probability that a randomly chosen newborn was delivered by emergency cesarean section and was also premature?

A student draws a card from a standard deck, does not replace it, and then draws a second card. Are the two draws independent or dependent events? Explain your reasoning.

A poll of $2000$ registered voters found that $850$ support a new environmental policy. If three voters are selected at random without replacement, what is the probability that all three support the new policy?

In an office, $8$ employees bring lunch from home, and $4$ order takeout. If two employees are randomly selected without replacement to join a wellness program about healthy eating, what is the probability that both bring lunch from home?

A jar contains $5$ red and $7$ blue marbles. You draw one marble, do not replace it, and then draw a second marble. Let event A be "the first marble is red" and event B be "the second marble is blue." Are these events dependent or independent?

A student participates in a spelling bee. Consider these events:

Event G: The student spells the most words correctly in a single round

Event H: The student is eliminated before the final round

Are these events mutually exclusive? Are they independent or dependent?

A lottery draws $5$ numbers without replacement from the integers $1\text{–}60$ and independently draws a separate bonus number from the integers $1\text{–}40$. A player picks one set of five numbers and one bonus number. What is the probability that a single ticket matches all six drawn numbers (the five main numbers and the bonus)?

A student selects a slip of paper labeled with a number from a box of $30$ slips, does not replace it, and then selects another slip. Are these two selections independent or dependent?

A patient receives a flu vaccine and then later contracts the flu. Are these two events independent or dependent?