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For two given events Aa n dB ,P(AnnB)i s...

For two given events `Aa n dB ,P(AnnB)i s` (a)not less than `P(A)+P(B)-1` (b)not greater than `P(A)+P(B)` (c)equal to `P(A)+P(B)-P(AuuB)` (d)equal to `P(A)+P(B)+P(AuuB)`

A

not less than P(A)+P(B)-1

B

not greater than P(A)+P(B)

C

equal to `P(A)+P(B)-P(A cup B)`

D

equal to P(A)+P(B)+P(A cup B)

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
We know that,
`P(AnnB)=P(A)+P(B)-P(AuuB)`
Also, `P(AuuB)le1`
`:. P(AnnB)_(min)," where "P(AuuB)_(max)=1`
`rArr P(AnnB)geP(A)+P(B)-1`
`:.` Option (a) is true.
Again, `P(AuuB)ge0`
`:. P(AnnB)_(max)," when "P(AuuB)_(min)=0`
`rArr P(AnnB)le P(A)+P(B)`
`:. `Option (b) is true.
Also, `P(AnnB)=P(A)+P(B)-P(AuuB)`, Thus, (c ) is also correct.
Hence, (a),(b),(c ) are correct options.
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