If M and N are two events such thqt P(N)=3/5, P(N|M)=2/3 and P(M'UN')=19/25. (a) Find P(M) (b)P(M|N)?

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Answer 1 · 2018-04-05T05:41:58

#M'uuN'# is given by the red part, therefore #(M'uuN')'# would be the white one.

#(M'uuN')' = MnnN#

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Now, it is given that,
#P(N)=3/5# #color(white)(ddwwd# #P(N|M)=2/3# #color(white)(dddww# #P(M'uuN')=19/25# so, #P(MnnN)=6/25#

(a) Find #P(M)#

We know. by conditional probability,
#P(N|M)= (P(MnnN))/(P(M)#

#=>P(M)= (6/25)/(2/3)#

#=>P(M)= (6/25)xx(3/2) = 9/25#

(b) Find #P(M|N)#

#P(M|N)= (P(MnnN))/(P(N)#

#=> (6/25)/ (3/5)#

#=> (6/25)xx(5/3) = 2/5#