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If A(1),A(2),……………,A(n) be any events of...

If `A_(1),A_(2),……………,A_(n)` be any events of the same sample space then

A

`P(A_(1) cup A_(2) cup ..cup A_(n))=P(A_(1))+P(A_(2))+..+P(A_(n))`

B

`P(A_(1) cup A_(2) cup..cup A_(n)) gt P(A_(1))+P(A_(2))+..+P(A_(n))`

C

`P(A_(1) cup A_(2) cup ..cup A_(n)) le P(A_(1))+P_(A_(2))+..+P(A_(n))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
For any two events A and B, we have
`P(A cup B)=P(A)+P(B)-P(A cap B)`
`implies P(A cap B) le P(A)+P(B)`
Using principle of matematical induction it can be easily proved that
`P(underset(i=1)overset(n)cupA_(i)) le underset(i=1)overset(n)sum P(A_(i))`
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  18. A lot consists of 12 good pencils , 6 with minor defects and 2 with ma...

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