Question

A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is

• A. ${ } ^ { 10 } C _ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 4 }$
• B. ${ } ^ { 10 } C _ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 6 }$
• C. ${ } ^ { 10 } C _ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 8 }$
• D. ${ } ^ { 10 } C _ { 6 } \left( \frac { 1 } { 2 } \right) ^ { 10 }$

Answer 1

Answer: (D)

${ } ^ { 10 } C _ { 6 } \left( \frac { 1 } { 2 } \right) ^ { 10 }$

Answer 2

Required probability

$= { } ^ { 10 } C _ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 6 } = { } ^ { 10 } C _ { 4 } \left( \frac { 1 } { 2 } \right) ^ { 10 }$ $= { } ^ { 10 } C _ { 6 } \left( \frac { 1 } { 2 } \right) ^ { 10 }$