Answer:
The probability (P) of selecting two quarters, with replacement, can be calculated by considering the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. Ricky is taking 2 coins at random from a total of 3 quarters, 5 dimes, and 2 nickels. Therefore, the total number of coins he can select is 3 + 5 + 2 = 10.
Since Ricky is replacing each coin after selecting it, the number of possible outcomes for each selection remains the same. Therefore, the total number of possible outcomes for selecting two coins is 10 * 10 = 100.
Next, let's determine the number of favorable outcomes. Ricky wants to select two quarters. Since there are 3 quarters in total, the number of ways he can select two quarters is given by the combination formula: C(3, 2) = 3! / (2! * (3-2)!) = 3.
Finally, we can calculate the probability (P) by dividing the number of favorable outcomes by the total number of possible outcomes: P = number of favorable outcomes / total number of possible outcomes.
P = 3 / 100 = 0.03 or 3%. Therefore, the probability of Ricky selecting two quarters, with replacement, is 0.03 or 3%