A box contains 10 fuses. Eight of them are rated at 10 amperes and the other two are rated at 15 A. Two fuses are selected at random. What is the probability that the first fuse is rated at 10 A? Given that the first fuse was rated at 10 A, what is the probability that the second fuse is rated at 10 A? What is the probability that the third fuse is rated at 15 A, given that the first and second fuses were rated at 10 A?
Random and without replacement from an ordinary deck of 52 playing cards, a hand of 13 cards is to be dealt. Find the conditional probability that the hand contains at least one king, given that there are four kings in the deck.
In a certain factory, machines produce 1%, 4%, and 2% defective springs, respectively. Of the total springs produced in the factory, Machine M produces 30%, Machine N produces 25%, and Machine O produces 45%. If one spring is selected randomly from the total springs produced in a given day and it is defective, determine the probability that it is produced by Machine N. (Hint: Use Bayes' Theorem)