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Let A ,B ,C be three events such that P(...

Let `A ,B ,C` be three events such that `P(A)=0. 3 , P(B)=0. 4 ,P(C)=0. 8 , P(AnnB)=0. 88 ,P(AnnC)=0. 28 ,P(AnnBnnC)=0. 09.` If `P(AuuBuuC)geq0. 75 ,` then show that `0. 23lt=P(BnnC)lt=0. 48.`

Text Solution

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Since `P(A uu B uu C) ge 0.75`, we have
`0.75 le P(A) + P(B) + P(C ) - P(A nn B) - P(B nn C) - P(A nn C) + P(A nn B nn C) le 1`
or `0.75 le 0.3 + 0.4 + 0.8 - 0.08 - P(B nn C) - 0.28 + 0.09 le 1`
or `0.75 le 1.23 - P(B nn C) le 1`
or ` -0.48 le - P(B nn C) le-0.23`
or `0.23 le P(B nn C) le 0.48`
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