Probability Theory in Quantitative Finance Interviews: Part 2
<p>The first approach is to consider the 13 different outcomes of the cards. To start, we know that there are four suits of cards, hearts, diamonds, spades, and clubs. In each suit, there are 13 cards, ranging from 2 to A. Therefore, each card has 1/13 probability. Let’s say you get a card with a value of 2, the probability of winning is 0/51, since all cards left in the deck are equal to are greater than 2, which will result in your loss; Similarly, the probability of winning is 4/51 if you got a card with a value of 3. This happens when the dealer picks a card with a value of 2;…; with a value of A, your probability of winning is 48/51, because you can only lose when the dealer picks another A. Ultimately, your probability of winning is:</p>
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