Mathematics

Problem

Four mutually exclusive and exhaustive events

E_{1},E_{2},E_{3},E_{4}

have probabilities given by

P(E_{1})=t, \; P(E_{2})=t+0.05, \; P(E_{3})=2t, \; P(E_{4})=0.15

. (i) Determine the value of

t

. (ii) Hence find

P(E_{3})

. (iii) State whether the set

\{P(E_{1}),P(E_{2}),P(E_{3}),P(E_{4})\}

constitutes a valid probability model and justify your answer briefly. a. (i) Value of

t

b. (ii)

P(E_{3})

c. (iii) Validity of the model with a brief reason