Answer:

The probability of rolling a specific number, such as number 3, on a fair six-sided dice is always 1/6, assuming the dice is not biased and all sides are equally likely to land face up.

To calculate the probability of rolling number 3 landing face up exactly 16 times in 24 rolls of a fair dice, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:

P(X=k) is the probability of getting k successes (in this case, 16 occurrences of number 3 landing face up),

n is the number of trials (in this case, 24 rolls of the dice),

k is the number of successes (in this case, 16 occurrences of number 3 landing face up),

p is the probability of success on a single trial (in this case, the probability of number 3 landing face up, which is 1/6), and ( n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials, and can be calculated as n! / (k! * (n-k)!), where ! denotes the factorial of a number.

Plugging in the values to the formula, we get:

P(X=16) = (24 choose 16) * (1/6)^16 * (1 - 1/6)^(24-16)

= (24 choose 16) * (1/6)^16 * (5/6)^8

Using a calculator or software that can calculate factorials and exponents, we can determine the numerical value of (24 choose 16) to be 735471, and we can plug in the other values to calculate the final probability.