Which of the following output is not expected from MS-excel function = RAND() ?

Question

Accepted Answer

The correct option is (2):

The Microsoft Excel function =RAND() is designed to return a uniformly distributed pseudo-random real number that is greater than or equal to 0 but strictly less than 1. This range is represented mathematically as the half-open interval $\[0, 1)$. The key conceptual detail here is that the upper boundary, 1, is explicitly excluded from the possible outputs. While the function can return a value infinitesimally close to 1, such as 0.99999999999999, it will never generate the exact integer value of 1 itself. Consequently, of all the choices provided, '1' is the only value that the standard, un-modified =RAND() function cannot mathematically produce, making it the correct answer for the value that is *not expected*.

The incorrect option is (1):
The value 0.73 is a real number that falls perfectly within the function's defined range, as $0 \le 0.73 \< 1$. Since the `=RAND()` function is set to generate any real number within this interval with equal probability, $0.73$ is a fully expected and valid result. You will commonly observe similar values when using the function, confirming that it adheres to the uniform distribution criteria.

The incorrect option is (3):
The value 0.01 is extremely close to the lower boundary of the range, which is 0. However, because $0 \le 0.01 \< 1$ is a true statement, 0.01 is a legitimate output of the `=RAND()` function. The function is capable of generating values down to zero (inclusive) and all small positive decimal numbers, making $0.01$ a perfectly possible, albeit less frequent, outcome compared to numbers closer to the mean of $0.5$.

The incorrect option is (4):
The value 0.99 is very close to the upper boundary of the range, which is 1. Since the function's output must be strictly less than 1, and $0.99$ satisfies this condition, it is a valid and expected output. Any number from zero up to, but not including, one, can be generated. As such, 0.99 is a perfectly ordinary random number the function might return.