A bag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies. If 2 coins are randomly chosen from the bag, one after th
e other, and not replaced, and if the total value of the chosen coins is 26 cents, what is the probability that a third coin randomly chosen from the bag will be a penny?
The two coins chosen have to be a quarter and a penny. That leaves you with three pennies. You originally had 14 coins. You took out two you now have 12.
The 2 coins that have a combined value of 26 cents are a quarter and a penny. That means that 1 quarter and 1 penny must have already been removed from the bag. For this reason, the bag now contains 1 quarter, 5 dimes, 3 nickels, and 3 pennies. Therefore, the probability that a third coin randomly chosen from the bag will be a penny is
