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Question: If three dice are thrown together, then the probability of getting 5 on at least one of them is...

If three dice are thrown together, then the probability of getting 5 on at least one of them is

A

125216\frac { 125 } { 216 }

B

215216\frac { 215 } { 216 }

C

1216\frac { 1 } { 216 }

D

91216\frac { 91 } { 216 }

Answer

91216\frac { 91 } { 216 }

Explanation

Solution

Required probability

=3C1(16)(56)2+3C2(16)2(56)+3C3(16)3(56)0=91216= { } ^ { 3 } C _ { 1 } \left( \frac { 1 } { 6 } \right) \left( \frac { 5 } { 6 } \right) ^ { 2 } + { } ^ { 3 } C _ { 2 } \left( \frac { 1 } { 6 } \right) ^ { 2 } \left( \frac { 5 } { 6 } \right) + { } ^ { 3 } C _ { 3 } \left( \frac { 1 } { 6 } \right) ^ { 3 } \left( \frac { 5 } { 6 } \right) ^ { 0 } = \frac { 91 } { 216 }