Final answer:
To calculate the minimal estimate for the total number of students (X), given the sports day participation, one sums the number participating in event A only, the total participating in event B (including those in all events), and those not participating, then subtracts any known overlaps. Without more information on the overlap between events, we cannot calculate the precise total, but we can estimate a minimum number of students which is 425.
Step-by-step explanation:
The question is asking you to find the total number of students (X) in the school given the participation data for a sports day. You're told the number of students who participated in event A alone (70), the total number of students that participated in event B (330), the number that participated in all three events (40), and the number that did not participate in any events (65).
To determine X, you need to account for these groups of students. However, since the question doesn't provide complete information on overlaps between events, or the number of students participating in the third event or in both A and B but not the third event, we cannot calculate the exact total number of students without making assumptions or having additional information.
Therefore, we can only calculate a minimal estimate of X by considering the unique participants and those who didn't participate at all:
- Number of students participating only in A: 70
- Number of students participating in three events (also included in the total for B): 40
- Number of students not participating in any event: 65
We add these together: 70 (from A only) + 330 (from B total, including those in all three events) + 65 (non-participants) = X.
But we must be careful not to double-count the 40 students who are included in the total for B. We subtract this overlap to avoid this:
70 + 330 + 65 - 40 = 425 students.
This value of 425 is a minimal estimate for X, assuming no other overlap between events besides the 40 students who participated in all three.