A combinatorial problem related to the classical probability

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 $\{1,2,\dots ,n\}$ . We show that $f(n)\le n+1$, and $f(n)=n+1$ if there exists a Hadamard matrix of order $n$.