Given that bag contains 5 red marbles and 3 black marbles

For at least one of the three marbles drawn be black, if the first marble is red

Then the following three conditions will be followed

(i) Second marble is black and third is red = E₁

(ii) Second and third, both marbles are black = E₂

(iii) Second marble is red and third marble is black = E₃

Let event R_n = drawing red marble in n^th draw

And event B_n = drawing black marble in n^th draw

And

Required probability, P(E)= P(E₁) + P(E₂) + P(E₃)