In a United State election, a political analyst believes that if Democrats win F

Question

In a United State election, a political analyst believes that if Democrats win Florida, their probability of win the election is 0.9 and if they lose Florida, the possibility of winning the election is 0.4. The analysis believes the possibility of the Democrats winning Florida is 0.3. Based on the analysis, answer the question. (i) What is the possibility of Democrats winning election overall? (ii) What is the possibility of the Democrats winning Florida if it is known that they won the electron?

Explanation / Answer

E: winning the election

F: winning Florida

P(E|F)=0.9

P(E| not F)=0.4

P(F)=0.3 therefore P(not F)=1-0.3=0.7

A) P(E)=P(E|F)*P(F)+P(E|not F)*P(not F)= 0.9*0.3+0.4*0.7 = 0.55

B) P(F|E)=P(E|F)*P(F)/(E)=0.9*0.3/0.55=0.49

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