The last one occurs once? No — we have only four positions. If one occurs twice, two others once, that’s 2+1+1 = 4, so the fourth is covered. So the fourth outcome (the unused one) doesn’t need to be chosen — it’s determined. - Redraw

Understanding the Context

Imagine a scenario where there are four potential outcomes — let’s call them A, B, C, and D. In one trial, outcomes repeat or combine in such a way that:

• One outcome (say, A) occurs twice,
  
• Each of the others (B, C, D) occurs once,
  
• Therefore, the total adds to 4: 2 + 1 + 1 + 1 = 5? Wait — correction: actually, only three outcomes total here: A(2), B(1), C(1), and D(0)? Or are we distributing four “choices” across outcomes where one is repeated?

Wait — clarify: If one outcome repeats (two times) and the remaining three outcomes occur once each, that totals 2 + 1 + 1 + 1 = 5 possible occurrences, but that exceeds four. So the real logic is simpler and more elegant.

The true setup: Only four total slots exist. One outcome occurs twice, the other three occur once each — that sums to 2 + 1 + 1 + 1 = 5? No — that’s five. Instead, the phrasing likely means:

Key Insights

> One outcome happens twice, and the other three occur once each — but only four outcomes exist in total. So the “fourth” outcome is not unused — it does not occur at all, and is logically determined as the unallocated slot that doesn’t actually materialize.

But that contradicts “four outcomes exist.” The correct interpretation is:

• There are four possible results,
  
• But in a single event, one result occurs twice,
  
• Each of the other three occurs once,
  
• Since two slots are taken by the repeated outcome and one each by the others: Yes, the total is 2 + 1 + 1 + 1 = 5 — unless one outcome is “unused,” meaning excluded.

Wait — likely the confusion lies in how outcomes are distributed among four categories.

Final Thoughts

The Correct Logic: One Outcome Occurs Twice, Others Once — the Fourth Is Redundant

Think carefully: if there are four distinct outcome slots, and one of the results repeats — say, outcome A appears twice — while B, C, and D each appear once — then:

• Total occurrences: A×2, B×1, C×1, D×1 → 2+1+1+1 = 5, which exceeds four possible outcomes.

Therefore, in probability modeling, the setup must be:

> Among four possible outcomes, one outcome occurs twice, the others once — but since only four positions exist in the sample space, the “fourth” position must remain empty (or unused), not duplicated.

Thus:

• Total outcomes each occurring = 1 (twice) + 3 (once) = 4 total activations, but only 4 positions exist meaningfully —
  
• The fourth outcome — the unused one — is logically determined as not manifesting, not chosen.