There are 3 recognisable ways a child goes wrong here — distinct patterns, not carelessness.
Each one below is a mistake our question bank was built to expose, written out the way you would actually hear it said out loud at home.
Knowing which one you are looking at is the whole job. "Check your answer" does not help a child who is confidently applying the wrong rule.
What you might hearIf it is in both circles, it cannot go in A or B.
For A union B, the student lists outcomes that are only in A or only in B, but drops outcomes that are in both events.
The student reads "or" as one event or the other, but not both. They do not yet see that union means every outcome in A, B, or both.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
What you might hearIt says A and B, so I wrote all of A and all of B.
For A intersect B, the student copies every outcome from A and every outcome from B instead of only the outcomes shared by both.
The student hears "and" as a cue to join both lists. They have not tied intersection to the shared part of two events.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
What you might hearA complement means the part of B that is not A.
For the complement of A, the student lists only outcomes outside A but inside event B, or only the named opposite event, instead of all outcomes in the sample space that are not in A.
The student treats complement as the leftover part of the current pair of events. They miss that the sample space sets the boundary.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
For each mistake above, Algo School gives you the words to say next — the specific response that corrects the thinking instead of just marking the answer wrong, plus practice aimed at that exact error.
See your child's own results — start free
The Venn diagram shows set Swimming and set Track with the number of outcomes in each region. How many outcomes are in exactly one of the two sets (in Swimming or Track but NOT in both)?
Answer 16.0
Generated by probability-alg2, a deterministic question engine — not written by an AI, and verified before any child sees it.
Look at what they SAY, not just what they wrote. Each mistake above includes the phrasing a parent typically hears — that sentence is usually the giveaway. In Algo School, the tutor recognises these patterns while your child is working and adapts the session around the one it sees.
Yes. We track 3 distinct approved mistake patterns for this concept, each one written up because it recurs — not because it is unusual. A child making one of them is doing something systematic, which is far easier to fix than random errors.
Respond to the thinking, not the answer. Algo School gives parents the specific wording for each mistake, then generates practice targeted at that error and shows you whether it actually cleared.
They are part of the same content library that drives practice: each one is reviewed and approved before it is used, and the Conditional Probability and Normal Distributions questions on this site are checked by an automated verification pass before a child is ever served them.
See the full curriculum map — every Common Core concept we cover, the verified question count, and what a child at this level should know.
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See your child's own results — start free