Random Variables

Question

In a card game, a player randomly selects 2 cards in succession from a 52-card bridge deck. The player receives a score of 10 if the second card is the same suit as the first, a score of 5 if the second card is the same color and different suit, and a score of 0 if the second card is a different color. Let the random variable X be the score and find the probability distribution of X. (Enter your probabilities as fractions.)
X     P(X)
0     
5
10

Answer 1

Hi Stephanie,

Let's assume we removed the 2 Jokers from the deck. After the first draw of whatever card is drawn, there are 51 cards left in the deck. Of these 51 cards, 26 are of the wrong color for a match by suit or color and pay off 0. With those 26 accounted for, there are 25 left and 13 of those are of the same color but not in the same suit and the other 12 are in the same suit. So under the column labeled "P(X)," you should have 26/51 (first row) 13/51 (second row) and 12/51 last row.

If the Jokers are in the deck then this becomes a bit harder because there are two possibilities to consider, a Joker is drawn as the first card or a Joker is not drawn as the first card. For now, let's just assume Jokers have been removed.

Please feel free to contact me with any questions if either this answer of the answer to the 8 cards question (or even both :)) is unclear.

Kind regards,
Hugh