Solution:

Given A box with ten black and eight red balls.

Total number of balls in box = 18

(i) Both balls are red.

Probability of getting a red ball in first draw

As the ball is replaced after first throw,

Hence, Probability of getting a red ball in second draw =

Now, Probability of getting both balls red

(ii) First ball is black and second is red.

Probability of getting a black ball in first draw

As the ball is replaced after first throw,

Hence, Probability of getting a red ball in second draw =

Now, Probability of getting first ball is black and second is red

(iii) One of them is black and other is red.

Probability of getting a black ball in first draw

After the initial toss, the ball is changed.
Hence, Probability of getting a red ball in second draw

Now, Probability of getting first ball is black and second is red
Probability of getting a red ball in first draw

As the ball is replaced after first throw,

Hence, Probability of getting a black ball in second draw =

Now, Probability of getting first ball is red and second is black Therefore, Probability of getting one of them is black and other is red:

= Chances of getting a black first ball and a red second ball + Chances of getting a red first ball and a black second ball

Answer: i) 4/9 ii) 20/81 iii) 40/81