# A couple of probability questions about Playing cards i REALLY need help with?

Please explain and show steps of how u reach the answer, i really want to learn and understand.

Answer as many as you can, Thanks.

1)A bridge hand consists of 13 cards (out of a 52 card deck) dealt at random.

(a) What is the probability that a bridge hand will contain no hearts?

(b) What is the probability that a bridge hand will contain only face cards

(ie will contain only jacks, queens, kings and aces)?

(c) What is the probability that a bridge hand will contain all four aces?

2)Find the probability of 2 triples and 2 pairs (eg KKKQQQ2255) in a 10

card poker hand.

3) Find the probability of getting 3 triples (eg 777JJJAAA) in a nine

card poker hand?

4) Suppose we are playing poker with 7 cards hands. what is the probability of having 3 pair (JJ QQ KK A)?

### 1 Answer

- JerryLv 79 years agoBest Answer
Here are the first two to get you started.

1) 52 C 13 possible bridge hands.

P(no hearts) = (39 C 13) / (52 C 13)

Choose all 13 cards from the 39 non-hearts.

b) There are 16 face cards, so choice is limited to only those cards.

(16 C 13) / (52 C 13)

c) Choose all 4 aces. Choose the other 9 cards from the 48 non-aces.

(4 C 4) * ( 48 C 9 ) / ( 52 C 13 )

2) There are 13 ways to choose first triple, 12 for the second triple, 11 for first pair, 10 for second pair.

There are (4 C 3) = 4 ways to choose each triple from the 4 cards of that rank.

There are (4 C 2) = 6 ways to choose a pair from the 4 cards of that rank.

(52 C 10) ways to choose a 10 card hand from a standard deck.

( 13 * 12 * 11 * 10 * (4 C 3) * (4 C 3) * ( 4 C 2 ) * ( 4 C 2 ) ) / (52 C 10)