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Let P(x) denote the probability of the o...

Let `P(x)` denote the probability of the occurrence of event `xdot` Plot all those point `(x , y)=(P(A),P(B))` in a plane which satisfies the conditions, `P(AuuB)geq3//4a n d1//8lt=P(AnnB)lt=3//8`

Text Solution

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`P(A uu B) ge (3)/(4) and (1)/(8) le P(A nn B) le (3)/(8)`
Hence,
`P(A) + P(B) - P(A nn B) le (3)/(4)`
implies `P(A) + P(B) ge (3)/(4) + P(A nn B) ge (3)/(4) + (1)/(8) = (7)/(8)`
`implies x + y ge (7)/(8)`
We know that
`P(A nn B) le 1`
`implies P(A) + P(B) le 1 + P(A nn B) le 1 + (3)/(8) = (11)/(8)`
`implies x + y le (11)/(8)`

The shaded part in the figure is the required region.
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