Final answer:
The probability that the sum of three randomly chosen real numbers between 0 and 1 is greater than 1/2 cannot be determined without further information.
Step-by-step explanation:
To find the probability that the sum of three randomly chosen real numbers between 0 and 1 is greater than 1/2, we need to consider the range of values that the three numbers can take. Each number can be any value between 0 and 1.
By representing the three numbers as x, y, and z, the condition that the sum is greater than 1/2 can be written as x + y + z > 1/2.
To visualize this, consider the volume of a unit cube where each axis represents one of the three numbers. The condition x + y + z > 1/2 represents the volume of the region above the plane x + y + z = 1/2 within the unit cube.
The probability is then equal to the ratio of the volume of this region to the volume of the unit cube. However, calculating this volume is not straightforward and requires advanced mathematical techniques. Therefore, we cannot determine the exact probability without further information.