Solve these questions using binomial distribution 1) A pair of dice is rolled 20 times. What is the probability that: a) double sixes are rolled exactly twice? b) at least two double sixes are rolled? 2) In a manufacturing process it is estimated that 0.1% of the products are defective. If a client places an order for 25 of the products what is the probability that at least one of them is defective? 3) A baseball player has a batting average of 0.320. If you were to predict the likelihood that he could have a game in which he has no hits in three times at bat. a) Determine the theoretical probability that he has no hits in three times at bat b) Determine the probability distribution for the number of hits per game. c) Calculate the batter's expected number of hits per game.

4) A game consists of rolling a pair of dice ten times. For each sum that equals either six, seven, or eight on the two dice, you win one dollar. If it costs five dollars to play the game, is this a fair game?