Bag 'P' contains 3 white, 2 red, 5 blue balls and bag 'Q' contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from ' P ' and is placed in ' Q '. If a ball is chosen from bag ' $Q$ ' at random, then the probability that it is a red ball is

• A

  $\frac{9}{50}$
• B

  $\frac{13}{45}$
• Correct answer
  C

  $\frac{16}{55}$
• D

  $\frac{12}{35}$

Solution

Using multiplication theorem of probability. Required probability $\begin{aligned} & =\frac{3}{10} \times \frac{3}{11}+\frac{2}{10} \times \frac{4}{11}+\frac{5}{10} \times \frac{3}{11} \\ & =\frac{9+8+15}{110}=\frac{32}{110}=\frac{16}{55} . \end{aligned}$

Hence, the correct answer is option: 'C'.