Question

A fair dice is tossed eight times. Probability that on the eighth throw a third six is observed is -

• A. $\frac { { } ^ { 8 } \mathrm { C } _ { 3 } 5 ^ { 5 } } { 6 ^ { 8 } }$
• B. $\frac { { } ^ { 7 } C _ { 2 } \cdot 5 ^ { 5 } } { 6 ^ { 8 } }$
• C. $\frac { { } ^ { 7 } C _ { 2 } \cdot 5 ^ { 5 } } { 6 ^ { 7 } }$
• D. None of these

Answer 1

Answer: (B)

$\frac { { } ^ { 7 } C _ { 2 } \cdot 5 ^ { 5 } } { 6 ^ { 8 } }$

Answer 2

Third six occurs on 8^th trial. It means that in first 7 trials we must exactly 2 sixes and 8^th trial must result in a 6.

\ required probability = ⁷C₂.(1/6)².(5/6)⁵.(1/6)

=