  In the classical probability model, let $f(n)$ be the maximum number of
pairwise independent events for the sample space with $n$ sample points. The
determination of $f(n)$ is equivalent to the problem of determining the maximum
cardinality of specific intersecting families on the set $\{1,2,\ldots,n\}$ .
We show that $f(n)\leq n+1$, and $f(n)=n+1$ if there exists a Hadamard matrix
of order $n$.
