Paragraph: A certain college student has to complete his Chemistry problem set and Maths problem set on the night of December 31^ st 2009 (both due on 1^ st January 2010). If the student works on his problem sets in the maths library, the probability of finishing his maths problem set that night is 95 % and the probability of finishing his chemistry problem set that night is 75 % . If the student works on his problem

Step-by-step solution

M : He works in maths library C : He works in chemistry library F : He finishes his both problem set. P(M)= 60 100 = 6 10 P(C)= 40 100 = 4 10 P(F / M)== P(F M) P(M) = 60 100 95 100 75 100 60 100 = 95 100 75 100 = 7125 10000 = 57 80 Ans.(i) (By multiplication rule) aligned & P(F / C)= 40 100 90 100 80 100 40 100 = 72 100 = 18 25 Ans.(ii) & P(F)=P(C F)+P(M F)=P(C) P(F / C)+P(M) P(F / M)= ( 4 10 18 25 )+ ( 6 10 57 80 )= 32 250 + 171 400 aligned (By using total law of porbability) P(M / F)= P(M) P(F / M) P(F) = P(M) P(