probability

Question

the events F and N are such that  (F) = 0.64, P(N) = 0.33 and P (for N) =0.84, Find the probability of Not N and Not F

Answer 1

P(F OR N)=P(F)+P(N)-P(F AND N); P(¬F)=1-P(F)=0.36; P(¬N)=1-P(N)=0.67.

P(F OR N)=0.84=0.64+0.33-P(F AND N), P(F AND N)=0.97-0.84=0.13.

P(¬F OR ¬N)=P(¬F)+P(¬N)-P(¬F AND ¬N), P(¬F AND ¬N)=P(¬F)+P(¬N)-P(¬F OR ¬N).

P(¬F OR ¬N)=P(¬(F OR N))=1-0.84=0.16.

P(¬F AND ¬N)=0.36+0.67-0.16=0.87.