A bin in discount store contains 100 blank cassette tapes, of which 10 are known to be defective. If six of the tapes are selected at random, what is the probability that exactly two of them are defective? at least one of them is defective?

If a sack contains eight blue marbles and ten red marbles, and you randomly select four, what is the probability that exactly two of your four marbles are blue?

A bag contains 100 bills, 80 of which are authentic bills and 20 of which are counterfeit bills. Bills are drawn randomly without replacement. What's the probability that exactly two counterfeit bills are drawn before the third authentic bill is drawn?

A bag contains 7 red marbles, 5 white marbles, and 10 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that exactly two of the marbles are red?

A deck consists of playing cards that can have one of 16 suits and one of 5 ranks. A hand is a set of five cards randomly selected from the deck. How many hands are a four of a kind (four cards with the same rank but different suits, and a fifth card that is a different rank from the other four)? What is the probability of the hand being a four of a kind?

A bowl contains six blue chips and three red chips. Three chips are to be drawn successively at random and without replacement. Find the probability that the first draw results in a red-chip (A), the second draw results in a blue-chip (B), and the third draw results in a blue-chip (C).

A shipment contains 12 igneous, 10 sedimentary, and 10 metamorphic rocks. If 5 rocks are selected at random, find the probability that exactly 3 are sedimentary. The probability that exactly 3 of the rocks are sedimentary is (Round to four decimal places as needed.)

Consider a group of 8 people. Among them, there is one pair of twins. These 8 people are taken into two different rooms, Room A and Room B, with four people to each room. If all  groups of four people are equally likely, find the probability that the twins will be sent into the sameroom.