Question

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red

Answer 1

There are 2 possible cases: first ball drawn is red or is black.

P(first ball black) = 6/10

P(first ball red) = 4/10

P(second ball red | first ball drawn is black) = 4/12

P(second ball red | first ball drawn is red) = 6/12 = 1/2

 

From total Probability Theorem

The probability of the second ball being red, P(R) = (4/10)×(1/2)+(6/10) ×(4/12)

= (1/5)+(1/5)

= 2/5

 

 

Probability that the drawn ball is red = 2/5.