A bag contains x red balls, y blue balls and z yellow balls. One ball at random is taken out andreplaced. A second ball at random is taken out and replaced.If the balls are identical in all respects except colour and are well mixed, what is the probability that the first ball was red and the second blue?

Answer:

4) C

Total number of balls = (x + y + z)

Probability of first ball being red  =          x        
                                                           x + y + z

Since the ball is replace, the total number of balls will remain the same, i.e., (x + y + z)

Probability of second ball being blue =         y        
                                                                x + y + z

Probability of first ball being red and second ball being blue:

     x          x          y       
x + y + z         x + y + z

        xy      
 (x + y + z)²