Question

A bag contains 3 balls of unknown colours. A ball is drawn and found to be white. Then find the probability that all balls in the bag are white is

• A. 1/3
• B. ¼
• C. 1/9
• D. ½

Answer 1

Answer: (D)

½

Answer 2

0	1	2	3
E0	E1	E2	E3

P(E₀) = P(E₁) = P(E₂) = P(E₃) = $\frac { 1 } { 4 }$

Let E be the event of drawing white ball

P(E/E₀) = 0, P(E/E₁) = $\frac { 2 } { 3 }$, P(E/E₃) = 1

P(E₃/E) = $\frac { P \left( E _ { 3 } \right) \cdot P \left( E / E _ { 3 } \right) } { \sum _ { k = 0 } ^ { 3 } P \left( E _ { k } \right) \cdot P \left( E / E _ { k } \right) } = \frac { \frac { 1 } { 4 } \times 1 } { 0 + \frac { 1 } { 4 } \times \frac { 1 } { 3 } + \frac { 1 } { 4 } \times \frac { 2 } { 3 } + \frac { 1 } { 4 } \times 1 }$

= $\frac { \frac { 1 } { 4 } } { \frac { 1 } { 12 } + \frac { 2 } { 12 } + \frac { 3 } { 12 } } = \frac { 1 } { 4 } \times \frac { 12 } { 6 } = \frac { 1 } { 2 }$ .