Three events

MATHEMATICS · Subjective · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

Three events

E

F

and

G

in the same sample space have probabilities

P(E)=0.5

P(F)=0.4

P(G)=0.3

P(E\cap F)=0.20

P(E\cap G)=0.15

P(F\cap G)=0.12

and

P(E\cap F\cap G)=0.06

. (i) Are the events pairwise independent? (ii) Are the events mutually independent? Give reasons for each answer.