Final answer:
To ensure at least one pair of persons has the same first initials using the English alphabet, you must select 27 persons, due to the Pigeonhole Principle, which states that if you have more items than pigeonholes, at least one pigeonhole must contain more than one item.
Step-by-step explanation:
To calculate the minimum possible number of persons one can randomly choose to ensure that at least some pair of persons will have the same first initials for their first names using the English alphabet, we can use the Pigeonhole Principle. The English alphabet has 26 letters. According to the Pigeonhole Principle, if we have n pigeonholes and more than n items to put in them, at least one pigeonhole must contain more than one item. In this context, the pigeonholes are the first initials of the first names, and the items are the persons chosen.
The minimum number of persons we need to choose to guarantee that at least two persons will have the same initial is 27, which is one more than the number of pigeonholes (initials). This is so because if we select 26 persons, each could potentially have a different initial. But upon selecting the 27th person, we run out of unique initials and thus are guaranteed that at least one initial is shared by at least two persons. Thus, we can confidently answer that the minimum number of persons needed to ensure at least a pair with the same first initials for their first names is 27.