# Thread: Probability (with Bridge Hands)

1. ## Probability (with Bridge Hands)

Hello this is my first posting so I hope I'm doing everything right!

Okay so here is the question
----------------------------
What is the probability that a Bridge Hande (13 cards) contains:
a) 4 spades, 5 hearts, 3 diamonds, and 1 club

c) a void? (at least one suit that is not represented)
-----------------------------

Now I think I answered the first one correctly, here it goes:
a) (13C4 * 13C5 * 13C3 * 13C1)/(52C13)
= 0.00538779

b) now im not sure for this one but (is it correct?)...
(39C13)/(52C13) = 0.01279094804

c) I thought that the answer to this would be the same as b) since one suit was not represented in b)
-------------------------------

Well thanks in advance to anyone who responds with some input, I'm not great at this stats stuff, and our prof is not giving great notes :S.

Hello this is my first posting so I hope I'm doing everything right!

Okay so here is the question
----------------------------
What is the probability that a Bridge Hande (13 cards) contains:
a) 4 spades, 5 hearts, 3 diamonds, and 1 club

c) a void? (at least one suit that is not represented)
-----------------------------

Now I think I answered the first one correctly, here it goes:
a) (13C4 * 13C5 * 13C3 * 13C1)/(52C13)
= 0.00538779

b) now im not sure for this one but (is it correct?)...
(39C13)/(52C13) = 0.01279094804

c) I thought that the answer to this would be the same as b) since one suit was not represented in b)
-------------------------------

Well thanks in advance to anyone who responds with some input, I'm not great at this stats stuff, and our prof is not giving great notes :S.
For C, you will have to consider all the possibilities (I Think) and sum them

For example, one possibility is that Two Suits Arnt Represented (And Two Are), and a way this can happen is to have All Clubs and one Diamond, so Spades and Hearts are not represented, thats one example.

Hello this is my first posting so I hope I'm doing everything right!

Okay so here is the question
----------------------------
What is the probability that a Bridge Hande (13 cards) contains:

c) a void? (at least one suit that is not represented)
-----------------------------

$\displaystyle P(no\ spades)=\frac{39}{52}\times \frac{38}{51} .. \frac{27}{40} \approx 0.0128$

Void:

$\displaystyle P(void)=4 \times P(no\ spades)$

RonL