# Do all the numbers belong to same slot in the Hashtable?

I was reading the CLRS. In the Hashing Chapter on page 262 a statement says: "For example, if we know that the keys are random real numbers $$k$$ independently and uniformly distributed in the range $$0 \leq k < 1$$, then the hash function $$h(k)= \lfloor km \rfloor$$."

Question: Does Uniformly distributed meant all numbers have equal probability. if so then all numbers have the same $$k$$ values and belong to the same slot.

So if we set the hash function to be $$h(k)=\lfloor{km}\rfloor$$, then each given element is equally likely to hash into any of the $$m$$ slots. (Refer to the definition of simple uniform hashing in page 259 CLRS)
Yes, it is true that each element with key $$k$$ will be hashed to the same slot. But the point is the elements are chosen uniformly independently, so they have the same probability to hash to any of the $$m$$ slots.
• @bmchaitu In reference to your first comment above, $k$ doesn't have anything to do with probability. It is simply a real number in the interval $[0, 1)$. Probability comes in only when you decide that each value $k$ is as likely as any other. Apr 4 '20 at 19:38