Given: A box containing 10 black and 8 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 =

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 =

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 :

= Probability of getting first ball is black and second is red + Probability of getting first ball is red and second is black

=