Probability that finally makes sense

Most probability errors are reading errors: 'and' vs 'or', with or without replacement. Noeta forces the setup to be explicit before any arithmetic happens.

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What this covers

Sample spaces and basic rules
Independent and mutually exclusive events
Conditional probability and Bayes' theorem
Tree diagrams and combinatorics
Expected value

Worked example

Problem

A bag holds 4 red and 6 blue marbles. Two are drawn without replacement. P(both red)?

1
First draw
P(red) = 4/10.
2
Update the bag
Without replacement, 3 red remain out of 9 marbles, so P(red | red) = 3/9.
3
Multiply the chain
(4/10) × (3/9) = 12/90.

Answer: 2/15 ≈ 0.133

Mistakes that cost marks

Reusing the original denominator after a draw without replacement.
Adding probabilities for events that are not mutually exclusive.
Confusing P(A|B) with P(B|A).

Questions students ask

Why is conditional probability so hard?

Because the wording hides which event is given. Noeta makes you restate the condition before solving, which removes most of the error.

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