Question

[15] 4. Let E and F be events of sample space S. Let P(E) = 0.3, P(F) = 0.6 and the P(EUF) = 0.7. a) Fill in all probabilities in the Venn diagram shown. S b) Find P(EnF). c) Find P(ENF). d) Find the P(E|F). e) Are E and F independent events? Justify your answer.

Answer 1

solution - Given the information a) PLE) Forf ACE 2-0.6 and PLEVEL-0.7 0.3 ES PCE) = 260:3 PET= 0.6 pEUF) = 0.7. PIEL + PUEDE06 PIEVF)=0.7. PCEDED = PLE) - P (ERE) ... PLEUE2 = PE2 +PLE) – Plen ) 0.7 - 0.3 +0.6 - PIEDE) 0. 7 5 0.9 – PIEDER PIEDER = 0.-07 PLEAF) = 00:27 PlenĒL = 0.3-0.2 I PIEDĒ) -0.1 I PeFt to find PCEDE), PLEVE) =PCE) FATE OPLE) -PL EDE) 0.1 03+0.– PLENE) 0.7. E og -PLEDER ...plenF2 = 0.9 -0.7 PPEENF) = 0.2

The formula for PCEE) ist PCE/F) - PC ENE) PLE) 0.2 0.6 PIEF) = 0.33 Two events A&B are said to be indepe. if P(ANB) = PLA)* PLB) By yoing above defination, PEEDF) = 0.2 0 PLE) *PLE) 0:3 *Out PLE)* Ple2 = 0.18 - foom Ole PlenF) E PLE)* PIF) 150 events Ege are not independent exents.