A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to be selected, then the probability distribution of X is given by

Step-by-step solution

Probability of drawing one black ball = ^3 C ₀ ( 3 7 )^0 ( 4 7 )^3= ( 4 7 )^3 Probability of drawing two black ball = ^3 C ₁ ( 3 7 )^1 ( 4 7 )^2=3 3 7 ( 4 7 )^2= 9 7 ( 4 7 )^2 Probability of drawing zero black balls = ^3 C₂ ( 3 7 )^2 ( 4 7 )^1=3 ( 3 7 )^2 4 7 = 12 7 ( 3 7 )^2 Probability of drawing three black balls = ^3 C ₃ ( 3 7 )^3 ( 4 7 )^0= ( 3 7 )^3