# Thread: probability

1. ## probability

let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset

2. Originally Posted by math8553
let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset
There are ${{n-1} \choose {r-1}}$ subsets of $\left\{ {1,2,3, \cdots ,n} \right\}$ that contain the element 1.

3. ## Reply

The number of subset of cardinality r is
${{n} \choose {r}}$
and the number of those that doesn't contain 1 is ${{n-1} \choose {r-1}}$ as Plato told you.
The probability of taking a set that doesn't contain 1 is ${{n-1} \choose {r-1}}/{{n} \choose {r}}$