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four fair dice D1, D2,D3 and D4 each hav...

four fair dice `D_1, D_2,D_3 and D_4` each having six faces numbered 1,2,3,4,5 and 6 are rolled simultaneously. The probability that `D_4` shows a number appearing on one of `D_1,D_2,D_3` is

A

`(91)/(216)`

B

`(108)/(216)`

C

`(125)/(216)`

D

`(127)/(216)`

Text Solution

Verified by Experts

The correct Answer is:
A
Required probability
=1-Probability that number on `D_(4)` is different from number on `D_(1),D_(2) " and " D_(3)`
`=1-((.^(6)C_(1)xx5^(3))/(6^(4)))=1-(125)/(216)=(91)/(216)`
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