To calculate the probability of each event, we use the formula for probability: probability = number of desired outcomes / number of total outcomes. For event A, we have 9 nickels and need to choose 2 without replacement. The number of ways to choose 2 nickels from 9 is calculated using combinations: (9 choose 2) = 36. The total number of ways to choose any 2 coins from 18 coins (6 pennies + 9 nickels + 3 dimes) is (18 choose 2) = 153. Thus, the probability of choosing 2 nickels is 36/153 = 0.23529411764705882. For event B, since we are replacing the coin after the first draw, the probability of choosing a nickel first is 9/18, and then the probability of choosing a dime is 3/18, leading to a combined probability of (9/18) * (3/18) = 0.08333333333333333. For event C, without replacement, the probability of choosing a nickel first is 9/18, and then the probability of choosing a dime from the remaining 17 coins is 3/17, resulting in a probability of (9/18) * (3/17) = 0.08823529411764706. For event D, the probability of choosing a penny first is 6/18, followed by choosing 2 nickels without replacement, which is (9/17) * (8/16), leading to a probability of (6/18) * (9/17) * (8/16) = 0.08823529411764705.