Final answer:
The probability that a dancer performs first in the talent competition is 4/13, calculated by dividing the number of dancers (8) by the total number of acts (26).
Step-by-step explanation:
The question asks for the probability that a dancer performs first in a randomly ordered talent competition with 6 instrumentalists, 12 singers, and 8 dancers. To solve this, we must consider the total number of acts, which is the sum of instrumentalists, singers, and dancers (6 + 12 + 8 = 26 acts).
The probability that a dancer performs first is the number of dancers divided by the total number of acts.
Therefore, the probability is 8 dancers out of 26 acts total, which simplifies to 4/13.