Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both the balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.
Given:
⇒ Bag contains 10 black balls and 8 red balls
It is told that two balls are drawn from bag with replacement.
Let us find the Probability of drawing each colour ball from the bag.
⇒ P(B1) = P(drawing black ball from bag)
⇒ 
⇒ 
⇒ 
⇒ P(R1) = P(drawing red ball from bag)
⇒ 
⇒ 
⇒ 
We need to find:
(i) P(Drr) = P(both balls drawn are red)
(ii) P(Dbr) = P(first drawn is black and next is red)
(iii) P(Srd) = P(one ball is red and other is black)
⇒ P(Drr) = P(both balls drawn are red)
Since drawing a ball is independent for each bag, the probabilities multiply each other.
⇒ 
⇒ 
⇒ 
⇒ P(Dbr) = P(first drawn is black and next is red)
Since drawing a ball is independent for each bag, the probabilities multiply each other.
⇒ 
⇒ 
⇒ 
⇒ P(Srb) = P(one ball is red and other is black)
⇒ P(Srb) = P(first drawn is red and next is black) + P(first drawn black and next is red)
⇒ P(Srb) = P(Drb) + P(Dbr)
Since drawing a ball is independent for each bag, the probabilities multiply each other.
⇒ 
⇒ 
⇒ 
⇒ 
∴ The required probabilities are 
.