(Solved): only do second part only do second part (a, b, c) (b) Suppose that a test for opium use has a \( 2 ...

(b) Suppose that a test for opium use has a \( 2 \% \) false positive rate and a \( 5 \% \) false negative rate. That is, \( 2 \% \) of people who do not use opium test positive for opium, and \( 5 \% \) of opium users test negative for opium. Furthermore, suppose that \( 1 \% \) of people actually use opium. (i) Find the probability that someone who tests negative for opium use does not use opium. (ii) Find the probability that someone who tests positive for opium use actually uses opium. (a) How many permutations of the letters LMNOPQRS contain the strings MON and NPS? (b) How many different strings can be made from the letters in AARDVARK, using all the letters? (c) A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and chia seed croissants. How many ways are there to choos (i) two dozen croissants with at least two of each kind? (ii) two dozen croissants with at least four cherry croissants and no more than 2 chia seed croissants?