Question

A card game is being played and the 7 of clubs, 9 of hearts, 10 of spades, and 10 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.)

Answer 1

A normal deck has 52 cards.

Our the deck has 4 cards less, 7 of clubs, 9 of hearts, 10 of spades, and 10 of hearts, so it has 48 cards.

To win the game, the card must be J, Q or K, so there are 12 cards available to win the game, so the probability is:

`\text{prob}=\frac{success\text{ cases}}{total\text{ cases}}=(12)/(48)=(1)/(4)`

The probability (or chance) to win the hand is 25% (1/4).