# Thread: Probability Basic

1. ## Probability Basic

In the game of bridge, each player is dealt 13 cars out of a deck of 52. determine the probability of a player receiving
a) all hearts
b) all hearts in ascending order
Can someone check my work? there arent any in my text

a)
13C13/52C13
b) 13P13/52C13

2. ye your spot on there

3. Hello john-1
Originally Posted by john-1
In the game of bridge, each player is dealt 13 cars out of a deck of 52. determine the probability of a player receiving
a) all hearts
b) all hearts in ascending order
Can someone check my work? there arent any in my text

a)
13C13/52C13
b) 13P13/52C13
Your answer to (a) is fine: the number of ways of choosing 13 cards from 52 is ${^{52}C_{13}}$. Just one of these consists of all 13 hearts. So the probability is $\frac{1}{{^{52}C_{13}}}$.

But I think you've confused things in part (b). The number of ways of choosing and arranging 13 cards from 52 is ${^{52}P_{13}}$, and again just one of these is all 13 hearts in ascending order. So the probability is $\frac{1}{{^{52}P_{13}}}$.

Grandad

4. Originally Posted by Grandad
So the probability is $\frac{1}{{^{52}P_{13}}}$.
While I agree that is most likely the expected answer, I would have said it is $\frac{2}{{^{52}P_{13}}}$.
The ace could be first or last.
At least that is true in poker. I do not know bridge.

5. Originally Posted by Plato
While I agree that is most likely the expected answer, I would have said it is $\frac{2}{{^{52}P_{13}}}$.
The ace could be first or last.
At least that is true in poker. I do not know bridge.
Yes, I realised that the phrase 'ascending order' could be ambiguous, but I assumed that, since it is bridge, aces were always high, and that there was therefore only one possibility.

Grandad