Probability - Getting dealt 3 of the same card in 5 Stud

[drexah]

What is the probability of, after recieving say the Jack of spades, that out of the next following 4 cards, two of them will be jacks? Suppose that you are the only person being dealt the cards.

[gaming_mouse]

The number of people being dealt cards will not affect the calculation.

There are 3 jacks left in the deck out of 51 cards total.

There are two possibilites:

1) 3 of the next 4 are jacks
2) 2 of the next 4 are jacks

There are 48 four-card hands fitting description 1).

There are 3*48*47 = 6768 four-card hand fitting description 2).

There are nCr(51,4)=249900 possible four-card hands possible given the J already in your hand.

Thus the chance you are looking for is:

(6768 + 48) / 249900 = .0272

Slighly under 3%

gm