Solution: This is a multinomial probability problem. Let $ X = (X_S, X_P, X_F) $ be the counts of each outcome in 12 independent trials, with probabilities $ p_S = 0.4 $, $ p_P = 0.3 $, and $ p_F = 0.3 $. The probability mass function of a multinomial distribution gives:

Mon, 04 May 2026 06:15:23 +0000

Content under review