Answer: C. The expected number of decays is the probability of decay per nucleus multiplied by the number of nuclei: $0.20 \times 500 = 100$ nuclei. Because decay is random, this is an expected number, not a guarantee of the exact number that will decay.

A: converts the probability 0.20 to 20% and reports 20 as the number of nuclei, without applying the probability to the sample of 500.
B: uses half the stated probability, 0.10, giving 50 nuclei.
D: calculates the expected number that do not decay, $0.80 \times 500 = 400$ nuclei.
Remember: probability predicts an expected fraction of a sample, not which individual nuclei decay.