Question

An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success

• A. $\frac { 4 } { 27 }$
• B. $\frac { 8 } { 27 }$
• C. $\frac { 16 } { 27 }$
• D. $\frac { 24 } { 27 }$

Answer 1

Answer: (C)

$\frac { 16 } { 27 }$

Answer 2

Probability of failure = $\frac { 1 } { 3 }$

Probability for getting success $= \frac { 2 } { 3 }$

∴ Required probability $= { } ^ { 4 } C _ { 4 } \left( \frac { 2 } { 3 } \right) ^ { 4 } \left( \frac { 1 } { 3 } \right) ^ { 0 } + { } ^ { 4 } C _ { 3 } \left( \frac { 2 } { 3 } \right) ^ { 3 } \left( \frac { 1 } { 3 } \right)$

$= \left( \frac { 2 } { 3 } \right) ^ { 4 } + 4 \left( \frac { 2 } { 3 } \right) ^ { 3 } \left( \frac { 1 } { 3 } \right) = \frac { 16 } { 27 }$.