Supposing we have a set of 176 items and i want to select 65 out of them, why can we say the probability of extracting each single item is 65/176?
And then after having extracted the first, the probability adjusts to 64/175?
2026-05-15 00:08:10.1778803690
Basic probability extraction form sample
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Your initial sample space has $176$ elements, of which $(65)$ are favorable. Similarly, if you are flipping a coin once, and computing the probability of a Heads, the sample space has $(2)$ elements, of which $(1)$ of them are favorable.
Under the assumption that the event of selecting a favorable item happens to succeed, then both the sample space and remaining number of satisfactory items changes.
The sample changes from $(176)$ to $(175)$, because (assuming that selection is done without replacement), the item selected initially is no longer part of the sample space.
Similarly, the number of favorable items changes from $(65)$ to $(64)$, under the assumption that on the first selection, one of the favorable items was removed.