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There are boxes labelled B(1),B(2), . . ...

There are boxes labelled `B_(1),B_(2), . . . .,B_(6)`. In each trial, two fair dice `D_(1)D__(2)` are thrown. If `D_(1)` shows j and `D_(2)` shows k, then j balls are put into the box the `B(k)`. After n trials, what is the probability that `B_(1)` contains at most one ball ?

A

`((5^(n-1))/(6^(n-1)))+((5^(n))/(6^(n)))((1)/(6))`

B

`((5^(n))/(6^(n)))+((5^(n-1))/(6^(n-1)))((1)/(6))`

C

`((5^(n))/(6^(n)))+n((5^(n-1))/(6^(n-1)))((1)/(6))`

D

`((5^(n))/(6^(n)))+n((5^(n-1))/(6^(n-1)))((1)/(6^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`B_(1) . . . . . . . . . . . . . . . . . .B_(6)`.

Required probability `=((5)/(6))^(n)+n((5^(n-1))/(6^(n-1)))((1)/(6))`
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