JEE Advanced2011MathematicsProbabilityActual
Paragraph: 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 . Question: The probability of the drawn ball from U₂ being white is
Options
- A13 30
- B23 30
- C19 30
- D11 30
Correct answer
B. 23 30
Step-by-step solution
Now, probability of the drawn ball from V ₂ being white is P (white/ V₂ ) aligned & . P (white/ V₂ ) & =P(H) ^3 C₁ ^5 C₁ ^2 C₁ ^2 C₁ + ^2 C₁ ^5 C₁ ^1 C₁ ^2 C₁ & +P(T) ^3 C₂ ^5 C₂ ^3 C₂ ^3 C₂ + ^2 C₂ ^5 C₂ ^1 C₁ ^3 C₂ . & .+ ^3 C₁ ^2 C₁ ^5 C₂ ^2 C₁ ^3 C₂ & Now, P ( white / V₂ )= 1 2 3 5 1+ 2 5 1 2 & + 1 2 3 10 1+ 1 10 1 3 + 6 10 2 3 = 23 30 & aligned