Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red.
(ii) First ball is black and second is red.
(iii) One of them is black and other is red.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red.
(ii) First ball is black and second is red.
(iii) One of them is black and other is red.

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