Manipal MET2015MathematicsProbability
Let u₁ and u₂ be two urns such that u₁ contains 3 white, 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 urn 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 . Then, 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
By total probability theorem, Required probability = 1 2 ( 3 5 1+ 2 5 1 2 )+ 1 2 ( ^3 C₂ ^5 C₂ 1+ ^2 C₂ ^5 C₂ 1 3 + ^3 C₁ ^2 C₁ ^5 C₂ 2 3 ) aligned & = 1 2 ( 3 5 + 1 5 )+ 1 2 ( 3 10 + 1 30 + 2 5 ) & = 2 5 + 1 2 ( 9+1+12 30 ) & = 2 3 + 22 60 = 24+22 60 & = 46 60 = 23 30 aligned