`A` and `B` are `2` events such that `P(A)=(3)/(4)` and `P(B)=(5)/(8)`. If `x` and `y` are the possible minimum and maximum values of `P(AnnB)`, then

Question

`A` and `B` are `2` events such that `P(A)=(3)/(4)` and `P(B)=(5)/(8)`. If `x` and `y` are the possible minimum and maximum values of `P(AnnB)`, then

`A` and `B` are `2` events such that `P(A)=(3)/(4)` and `P(B)=(5)/(8)`. If `x` and `y` are the possible minimum and maximum values of `P(AnnB)`, then the value of `a+b` is
A. `0.5`
B. `0.8`
C. `0.9`
D. `1`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
`(d)` `AnnBsubB`
`P(AnnB) le P(B)`……….`(i)`
`P(AnnB) ,e (5)/(8)`
Now `P(AuuB) =P(A)+P(B)-P(AnnB)`
`P(AuuB) le 1`
`impliesP(A)+P(B)-P(AnnB) le 1`
`impliesP(AnnB) ge (3)/(4)+(5)/(8)-1`
i.e., `P(AnnB) ge (3)/(8)`……`(ii)`
From `(i)` and `(ii)`
`(3)/(8) le P(AnnB) le (5)/(8)`
`:.a+b=(3)/(8)+(5)/(8)=1`