Final answer:
The probability of overlap is 0.4545 or 45.45%.
Step-by-step explanation:
To find the probability that the line segments overlap, we need to determine the range of possible positions for the midpoints of the segments and calculate the probability of overlap within that range.
The first midpoint can be between the values of 0 and 11, and the second midpoint can be between 6 and 22.
To calculate the probability of overlap, we need to find the intersection between these ranges. The range of possible positions for the overlapping segment is the intersection between the two ranges, which is from 6 to 11.
The length of this range is 11 - 6 = 5 units.
The total range of possible positions for the midpoints of the segments is 11 - 0 = 11 units for the first segment and 22 - 6 = 16 units for the second segment.
Since both segments have the same length of 2 units, the probability of overlap is the ratio of the length of the overlapping range to the total range of possible positions.
Therefore, the probability of overlap is 5 / 11 = 0.4545 or 45.45%.