Final answer:
The probability of removing a blue coin is 5/7.
Step-by-step explanation:
To find the probability that the removed coin is blue, we need to consider the total number of coins and the number of blue coins in the bag. In this case, the bag contains 10 blue coins and four red coins, making a total of 14 coins. Since a coin is removed and replaced by another coin, the probability remains the same for each draw. Therefore, the probability of removing a blue coin is 10/14 or 5/7.