You have a deck of cards containing 26 black and 13 red cards. You pull out 2 cards at the same time and check their color. If both cards are the same color, then a black card is added to the deck. However, if the cards are of different colors, then a red card is used to replace them. Once the cards are taken out of the deck, they are not returned to the deck, and thus the number of cards in the deck keeps reducing. What is the probability the last card left in the deck is black?
my attempt:
for both cards are the same colors: (both black)+(both red)
((26/39)(25/38)) + ((13/39)(12/38))=0.5438
the cards are of different colors: (black +red)+(red +black)
((26/39)(13/38))+((13/39)(26/38))=0.4561
please let me know how to continue for the answer for:
What is the likelihood the last card left in the deck is black?
Best Answer
Hint: At the end of a turn, the number of red cards is always odd.