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There are n turns each continuous (n+1) ...

There are n turns each continuous (n+1) balls such that the ithurn contains 'I' white balls and (n+1-i) red balls. Let `u_(1)` be the event of selecting ith urn, i=1,2,3……..n and W denotes the event of getting a white balls.
If ` P(u_(i)) prop i`, where i=1,2,3,........,..n, then `lim_(n to oo) P(W)` is equal to

A

1

B

`(2)/(3)`

C

`(1)/(4)`

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `P(u_(i))=ki,Sigma P(u_(i))=1`
`rArr K=(2)/(n(n+1))`
`underset(nrarroo)limP(W)=underset(nrarroo)lim sum _(i=1)^(n)(2i^(2))/(n(n+1)^(2))`
`=underset(nrarroo)lim(2n(n+1)(2n+1))/(6n(n+1)^(2))=(2//3)`
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