A circular dartboard has a radius of 10 inches. The bullseye at the center is a circle with a radius of 2 inches. If a dart lands at a random point on the board, what is the probability it lands in the bullseye?

A factory uses two machines. Machine A produces 60% of all items and has a 5% defect rate. Machine B produces the remaining 40% and has a 3% defect rate. If a randomly selected item is found to be defective, what is the probability it was produced by Machine A?

A college program received 120 applications. The results are shown below. \[\begin{array}{|c|c|c|c|c|} \hline & \textbf{Accepted} & \textbf{Waitlisted} & \textbf{Rejected} & \textbf{Total} \\ \hline \textbf{In-state} & 30 & 15 & 15 & 60 \\ \textbf{Out-of-state} & 10 & 20 & 30 & 60 \\ \hline \textbf{Total} & 40 & 35 & 45 & 120 \\ \hline \end{array}\] Two applicants are selected at random without replacement. Given that the first applicant selected is an accepted in-state student, what is the probability the second applicant selected is also an accepted in-state student?

In a group of 200 adults, 100 exercise regularly. Of those who exercise regularly, 80% report good sleep quality. Of those who do not exercise regularly, 50% report good sleep quality. If an adult from the group is selected at random and reports good sleep quality, what is the probability that this person exercises regularly?