diff --git a/test/hyperparam/one_dimensional_range_methods.jl b/test/hyperparam/one_dimensional_range_methods.jl
index 386cadf4..2ffd8101 100644
--- a/test/hyperparam/one_dimensional_range_methods.jl
+++ b/test/hyperparam/one_dimensional_range_methods.jl
@@ -233,31 +233,31 @@ end
 @testset "NominalSampler" begin
 
     r = range(Char, :(model.dummy), values=collect("cab"))
+    N = 10000
 
-    @testset "probability vector specified" begin
-        s = MLJBase.sampler(r, [0.1, 0.2, 0.7])
-        rng = StableRNG(600)
-        dict = Dist.countmap(rand(rng,s, 1000))
-        c, a, b = map(x -> dict[x], collect("cab"))
-        @test a == 201 && b == 714 && c == 85
+    # to compute half-width of 95% confidence intervals, for counts of a Bernoulli process
+    # with probability `p`, sampled `N` times:
+    halfwidth(p, N) = 1.96*sqrt(p*(1 - p))*sqrt(N)
 
-        rng = StableRNG(89);
-        dict = Dist.countmap(rand(rng, s, 1000))
-        c, a, b = map(x -> dict[x], collect("cab"))
-        @test a == 173 && b == 733 && c == 94
+    @testset "probability vector specified" begin
+        p = Dict('c'=>0.1, 'a'=>0.2, 'b'=>0.7)
+        rng = StableRNG(660)
+        s = MLJBase.sampler(r, [p[class] for class in "cab"])
+        counts = Dist.countmap(rand(rng,s, N))
+        for class in "abc"
+            μ = p[class]*N
+            @test abs(counts[class] - μ) < halfwidth(p[class], N)
+        end
     end
 
     @testset "probability vector unspecified (uniform)" begin
         s = MLJBase.sampler(r)
-        rng = StableRNG(55)
-        dict = Dist.countmap(rand(rng,s, 1000))
-        c, a, b = map(x -> dict[x], collect("cab"))
-        @test a == 361 && b == 335 && c == 304
-
-        rng = StableRNG(550)
-        dict = Dist.countmap(rand(rng, s, 1000))
-        c, a, b = map(x -> dict[x], collect("cab"))
-        @test a == 332 && b == 356 && c == 312
+        rng = StableRNG(660)
+        counts = Dist.countmap(rand(rng,s, N))
+        for class in "abc"
+            μ = N/3
+            @test abs(counts[class] - μ) < halfwidth(1/3, N)
+        end
     end
 
 end