In a poll of $800$ residents, $35\%$ support a new city park. If two residents are randomly selected without replacement, what is the probability that neither supports the new city park?

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?

A fast-food restaurant offers $4$ types of meals: Burger Meal, Chicken Meal, Vegetarian Meal, and Fish Meal. Based on past data, the probability that a customer orders each type is as follows:

Burger Meal: $\frac{3}{10}$, Chicken Meal: $\frac{2}{10}$, Vegetarian Meal: $\frac{4}{10}$, Fish Meal: $\frac{1}{10}$

Twelve customers place their orders independently. What is the probability that exactly $4$ order Burger meals, $3$ order Chicken meals, $4$ order Vegetarian meals, and $1$ orders a Fish meal?

A straight flush is five consecutive ranks all in the same suit (the sequence Ace–$2$–$3$–$4$–$5$ is allowed and Ace-high straight is allowed). What is the probability of being dealt a straight flush (including the royal flush) in a $5$-card hand?

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