What versions are you using? These versions seem to work:
julia> rand(Categorical([1//2,1//2]))
2
(jl_waVJwl) pkg> st
Status `/tmp/jl_waVJwl/Project.toml`
[31c24e10] Distributions v0.24.12
julia> versioninfo()
Julia Version 1.6.0-rc1
Commit a58bdd9010 (2021-02-06 15:49 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, skylake)
Environment:
JULIA_REVISE_INCLUDE = 1