Math Help - Another Card Question

1. Another Card Question

1) Cards are dealt, one at a time, from a standard 52 card deck.
a) if the first 2 cards are both spades, what is the probability that the next 3 are also spades?

2) 5 cards are drawn from a standard 52 card deck. What is the probability that all 5 cards will be from the same suit?

3) A gambler has been dealt 5 cards: 2 are aces, one is a king, one a 5 and one 9. He discards the 5 and 9 and is dealt 2 more cards. What is the probability that he ends up with a full house?

For 1) all I know is that it's a conditional probability, but I have no clue what values to take

For 2) is it $\frac{4}{2,598,960}$ since it's $\binom{52}{5}$ and there are 4 possible suits.

For 3) I'm stuck on the values that I have to pick. Is it $\binom{47}{2} = 1081$ for the denominator, and $\binom{2}{1} \ \binom{3}{1}$ for the numerator, which equals $\frac{6}{1081}$ ?

2. Originally Posted by lllll
1) Cards are dealt, one at a time, from a standard 52 card deck.
a) if the first 2 cards are both spades, what is the probability that the next 3 are also spades?
?
Two spades dealt, conditional probability next card a spade is 11/50,

Two spades dealt, conditional probability next two cards are spades is (11/50)(10/49),

Two spades dealt, conditional probability next three cards are spades is (11/50)(10/49)(9/48).

RonL

3. Originally Posted by lllll
2) 5 cards are drawn from a standard 52 card deck. What is the probability that all 5 cards will be from the same suit?
Probability of 5 spades is (13/52)(12/51)(11/50)(10/49)(9/48)

as there are 4 suits altogether the probability that all cards are of the same suit is for times this.

RonL

4. Originally Posted by lllll
3) A gambler has been dealt 5 cards: 2 are aces, one is a king, one a 5 and one 9. He discards the 5 and 9 and is dealt 2 more cards. What is the probability that he ends up with a full house?
He has 2A and 1K in his hand, he needs to draw either 1A and 1K or 2K to get a full house.

At this point the remaining deck nominaly has 47 cards of which 2 are A's and 3 are K's

Take it from there.

RonL