A sample space S consists of three mutually exclusive and exhaustive events E₁, E₂ and E₃
MATHEMATICS · Single correct · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
A sample space S consists of three mutually exclusive and exhaustive events E₁, E₂ and E₃. A student assigns probabilities P(E₁)=0.3, P(E₂)=0.5 and P(E₃)=0.4. Determine the validity of this assignment.
(a) Valid because the probabilities satisfy P(E1)+P(E2)+P(E3)=1.
(b) Invalid because the probabilities sum to a value greater than 1.
(c) Valid because all probabilities are non-negative.
(d) Invalid because one of the probabilities exceeds 0.5, which is not allowed for three events.