Mathematics

Problem

For two events

E

and

F

of a sample space, it is given that

P(E)=0.35

P(F)=0.55

and

P(E|F)=\dfrac{7}{11}

. a. (i) Find

P(E\cap F)

. b. (ii) Hence, calculate

P(F|E)

. c. (iii) Using your results, decide whether the events

E

and

F

are independent, showing all necessary working.