Question

Probability Question

Answer 1

(this is a scenario I saw in a TV show and I was curious about the math behind it)

Two people are playing an (unfair) card game. There are two cards: one is a normal black Joker and the other is a misprinted card with two backs to it (it doesn't have a number or face on it). Player A is assigned to the misprinted card and player B is assigned to the normal card.


The two cards are mixed into the bag, and one card is pulled out. If the joker side is face up, the card is mixed back in and the game restarts. If the back of the card is face up, then the card is flipped over. If the joker side is face up, player B gets a point. If the backside is face up (meaning that the misprinted card was drawn) player A gets a point. First person to 10 points wins.

Answer 2

Now, I understand that the card game highly favors player A because of the "put the card back in if the joker side is up" condition. But what is the probability of player B winning?

Answer 3

My attempt at a solution: player A has a 2/3 chance of winning each individual round, while player B has a 1/3 chance of winning each round. There are 10 conditions in which player B can win:

Player B has 10 points, player A has 9 points
Player B has 10 points, player A has 8 points, etc. until we get
Player B has 10 points, player A has 0 points

Answer 4

So how would I set up the calculations? @sillybilly123 @sweetburger

Answer 5

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