If the probability that an event will occur is 0.83, then the probability that the event will not occur is:

By the complement rule of elementary probability, the sum of the probability of an event (P) and the probability of its complement (P̅) equals 1. P + P̅ = 1 Given P = 0.83, P̅ = 1 – 0.83 = 0.17. Therefore, the probability that the event will not occur is 0.17, corresponding to option A.

B. 0.07 – 1 − 0.83 ≠ 0.07; arithmetic error.
C. 0.6889 – Square of 0.83, not the complement.
D. 1.20 – Probabilities cannot exceed 1; violates probability axioms.
E. 83% – This is the given probability of occurrence, not non-occurrence.

1. Montgomery

D. C. & Runger

G. C. Applied Statistics and Probability for Engineers

7th ed.

Wiley

2019

Sect. 2.2 “Rules of Probability

” p. 49.

2. T. Pyzdek & P. Keller. The Certified Six Sigma Black Belt Handbook

3rd ed.

ASQ Quality Press

2018

Chap. 7 “Basic Probability

” p. 275–276 (Complement Rule).

3. MIT OpenCourseWare

Course 6.041/6.431 Probabilistic Systems Analysis

Lecture Notes 2

“Complementary Events

” pp. 2–3.