1.

यदि घटनाएँ इस प्रकार है कि `P(A) = (1)/(2), P(B) =(1)/(3)` तथा `P(A uu B) = (2)/(3)` क्या घटनाएँ A तथा B स्वतंत्र है ?

Answer» ज्ञात है, `P(A) = (1)/(2), P(B) = (1)/(3)` तथा `P(A uu B) = (2)/(3)`
`therefore` हम जानते है कि
`P(A uu B) = P(A) + P(B) - P( P nn B)`
`(2)/(3) = (1)/(2)+(1)/(3) - P(A nn B)`
`therefore " " P(A nn B) = (1)/(2)+(1)/(3) - (2)/(3)`
`= (3+2-4)/(6)`
`P(A nn B) = (1)/(6)`
अब `" " P(A).P(B) = (1)/(2) xx (1)/(3) = (1)/(6)`
अतः `" "n P(A nn B) = P(A).P(B)`
इसलिए घटनाएँ A तथा B स्वतंत्र है |


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