Mathematics

Mathematics

Problem

Events

E

and

F

in a probability experiment satisfy

P(E)=0.6

,

P(F)=0.5

and

P(E\cap F)=0.28

. A third event

G

is such that

P(G\mid E\cap F)=0.7

and

P(G\mid E\cap F^{c})=0.4

. a. (i) Verify whether

E

and

F

are independent events. b. (ii) Find

P(E\mid F)

and

P(F\mid E)

. c. (iii) Calculate the probability that all three events

E

,

F

and

G

occur together.

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