Question

A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is.

• A. $\frac { 8 } { 141 }$
• B. $\frac { 10 } { 243 }$
• C. $\frac { 11 } { 243 }$
• D. $\frac { 8 } { 41 }$

Answer 1

Answer: (C)

$\frac { 11 } { 243 }$

Answer 2

Probability for white ball $= \frac { 2 } { 6 } = \frac { 1 } { 3 }$

Probability for black ball $= \frac { 4 } { 6 } = \frac { 2 } { 3 }$

$\therefore$Required probability

$= { } ^ { 5 } C _ { 5 } \left( \frac { 1 } { 3 } \right) ^ { 5 } \left( \frac { 2 } { 3 } \right) ^ { 0 } + { } ^ { 5 } C _ { 4 } \left( \frac { 1 } { 3 } \right) ^ { 4 } \left( \frac { 2 } { 3 } \right)$

$= \left( \frac { 1 } { 3 } \right) ^ { 4 } \left[ \frac { 1 } { 3 } + 5 \cdot \frac { 2 } { 3 } \right]$ $= \frac { 11 } { 3 ^ { 5 } } = \frac { 11 } { 243 }$.