1.

यदि `P(A)=3/8, P(B)=1/2` तब `P(bar(A)/bar(B))` और `(bar(B)/bar(A))` ज्ञात कीजिए।

Answer» यहाँ, `P(A) =3/8, P(B)=1/2`
`P(A nn B)=1/4`
चूँकि `P(bar(A)/B)=(P(bar(A) nn bar(B)))/(P(bar(B)))` ...(1)
और `P(bar(B)/bar(A))=(P(bar(A) nn bar(B)))/(P(bar(A)))` ...(2)
अब हम `P(bar(A)), P(bar(B))` और `P(bar(A) nn bar(B))` का मान ज्ञात करेंगे।
`P(bar(A))=1-P(A)=1-3/8=5/8`
`P(bar(B))=1-P(B)=1-1/2=1/2`
`P(bar(A) nn bar(B))=P(bar(A uu B))`, [डी-मॉर्गन नियम से]
`=1-P(A uu B)`
`=1-{P(A)+P(B)-P(A nn B)}`
`=1-(3/8+1/2-1/4)`
`=1-5/8=3/8` ...(3)
`:. P(bar(A)/bar(B))=(P(bar(A)nnbar(B)))/(P(bar(B)))=(3//8)/(1//2)=3/4`
और `P(bar(B)/bar(A))=(P(bar(A) nn bar(B)))/(P(bar(A)))=(3//8)/(5//8)=3/5`.


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