pr.probability – Probability of 2nd marble picked from a bag being same color as 1st marble picked

Say I have a bag of 20 marbles. 9 are white and 11 are black. I pick a marble from the bag, observe the color and place it back into the bag. I then pick another marble from the bag. How would I work out the probability of the 2nd marble being the same color as the first marble ?

What I know so far about the 1st marble…

  • prior probability of it being white is 0.45, and black 0.55
  • conditional probability of white 0.2, and black 0.3
  • total probability of it being white 0.255, and black 0.745