If P(A)=1/4,P(B)=1/3 and P(A∪B)=1/2 find the values of 1. P(A∩B) 2. P(A∩B') 3. P(A'∩B') ?

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P(A∩B)

P(A∩B')

P(A'∩B')

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Answer 1 · 2018-04-20T05:46:31

Please, see the explanation below

#P_A=1/4#, #=>#, #P_barA=1-1/4=3/4#

#P_B=1/3#, #=>#, #P_barB=1-1/3=2/3#

#P_(AuuB)=1/2#

#P_(AuuB)=P_A+P_B-P_(AnnB)#

Therefore,

#P_(AnnB)=P_A+P_B-P_(AuuB)#

#=1/4+1/3-1/2#

#=3/12+4/12-6/12#

#=1/12#

#P_(AnnbarB)=P_AxxP_A(barB)#

#=1/4xx2/3#

#=1/6#

#P_(barAnnbarB)=P_barAxxP_barA(barB)#

#=3/4xx2/3#

#=1/2#