Probability: common misconceptions

If your child says… “All four outcomes still belong in the denominator.”

Ask together

Can outcome 1 still qualify after you learn the number exceeds 1?

What’s true

The condition leaves three equally likely outcomes; only these belong in the denominator.

If your child says… “The second black chance stays the same.”

Ask together

After black leaves, how many black balls remain among how many balls?

What’s true

Removing a black ball reduces both the black count and the total.

If your child says… “Events that cannot happen together must be independent.”

Ask together

If the die is even, does odd retain its original chance?

What’s true

For events with positive chances, mutual exclusion makes them dependent.

If your child says… “At least one head means exactly one head.”

Ask together

Does a result with two heads contain at least one head?

What’s true

At least one includes every result containing any heads.

If your child says… “The groups must have equal chances.”

Ask together

Would unequal group chances leave any result unclassified?

What’s true

A partition needs complete coverage, no overlap and a positive chance for each group.

If your child says… “Just average the working fractions of the batches.”

Ask together

Are you equally likely to select either batch when choosing among all six pens?

What’s true

A larger batch contributes more possible selections, so its working fraction needs greater weight.

If your child says… “Every defective item was flagged, so every flagged item is defective.”

Ask together

Which sound item also appears among the flags?

What’s true

A flag means counting among flagged items, while a defect means counting among defective items.

If your child says… “Four outcomes must give four different values.”

Ask together

What head count do HT and TH each give?

What’s true

Several outcomes can receive the same number.