A card game is being played and the 4 of hearts, 8 of clubs, and 9 of hearts
are drawn. In order to win the hand, the next card must be higher than the
highest card already on the table. Assuming the game is played with a single
deck, what is the chance that the next card drawn will win the hand? (An ace
has a value of 1.)
+1224 There are 52 - 3 = 49 cards remaining, since the 4 of hearts, 8 of clubs, and 9 of hearts have already been drawn. We need the next card drawn to be higher than a 9. Out of the possible values, the next card could be a 10, J, Q, or K (assuming face cards are greater than 10).
In that case, there are 4 * 4 = 16 possible cards that would give a winning hand for a probability of 16/49.
