Question

A box A contains 3 red balls and 4 blue balls, box B contains 4 red balls and 3 blue balls. A ball is randomly taken from box A and kept in box B. If a ball is drawn from box B, what is the probability that the ball drawn is a red ball?

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

The following situations will come:

(i) Red ball is drawn from box A and then kept in box B, then red ball is picked from the box B

Probability of drawing a red ball from box A = $\frac{3}{7}$

Then probability of drawing a red ball from box B after putting the red ball drawn from box A = $\frac{5}{8}$

(ii) Blue ball is drawn from box A and then kept in box B, then red ball is drawn from box B

Probability of drawing a blue ball from box A = $\frac{4}{7}$

Then probability of drawing a red ball from box B after putting the blue ball drawn from box A =$\frac{4}{8}$

Total probability =$\left(\frac{3}{7}\right)\left(\frac{5}{8}\right)+\left(\frac{4}{7}\right)\left(\frac{4}{8}\right)$

$=\left(\frac{31}{56}\right)$