Discussion Forum

Let U₁ and U₂ be two urns such that U₁ contains 3 white and 2 red balls and U₂ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears then 2 balls are drawn at random from U₁ and put into U₂. Now, 1 ball is drawn at random from U₂

Given that the drawn ball from U₂ is white. the probability that head appeared on the coin is

Answer:

Explanation:

P( head appeared /white from $V_{2}$)

 =$P(H).\frac{\left\{\frac{^{3}C_{1}}{^{5}C_{1}}\times\frac{^{2}C_{1}}{^{2}C_{1}}+\frac{^{2}C_{1}}{^{5}C_{1}}\times\frac{^{1}C_{1}}{^{2}C_{1}}\right\}}{\frac{23}{30}}$

 =$\frac{1}{2}\frac{\left\{\frac{3}{5}\times1+\frac{2}{5}\times\frac{1}{2}\right\}}{\frac{23}{30}}=\frac{12}{23}$