Question

A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?

Answer 1

Bag contains 5 red marbles and 3 black marbles, 
For atleast one of the three marbles drawn be black, if the first marble is red,
then the following situations are possible 
Event E₁ = Second marble is black and third is red 
Event E₂ = Second marble is black and third is also black (E₂)
Event E₃ = Second marble is red and third is black (E₃)
Let Event R_i = drawing red marble in ith draw 
Event B_i = drawing black marble in ith draw