Let A, B, and C be independent events which occur with probabilities 0.8, 0.5, and 0.3 respectively. The probability of occurrence of at least one of the events is _______

GATE 1994 · Engineering Mathematics · Independent Events · medium

Answer: 0.93

1. Complement probabilities: P(A') = 1 - 0.8 = 0.2; P(B') = 1 - 0.5 = 0.5; P(C') = 1 - 0.3 = 0.7.
2. Probability none occur: P(none) = 0.2 * 0.5 * 0.7 = 0.07.
3. At least one occurs: P(A union B union C) = 1 - 0.07 = 0.93.