Card Draw Probability Tree

Card draw probability tree

This probability tree represents two dependent card draws. The first draw changes the deck available for the second, so the probabilities below Heart differ from those below Non-heart. That is the key reason to use a tree: each later probability belongs to the earlier branch that led to it. The rounded values keep the diagram readable; a classroom version can replace them with exact fractions from a 52-card deck. Follow a path to describe an ordered outcome, then multiply the branch probabilities to calculate its probability. This pattern works for any sample drawn without replacement. It gives readers a concise reference they can reuse when discussing the result with colleagues.

Type Arbre de décisionNorme Howard-Raiffa / CART-sklearn / taxonomyMoteur schematex-decisiontreeMis à jour 24/09/2026

La demande

“A probability tree for drawing two cards without replacement: first card Heart or Non-heart, then the second card Heart or Non-heart, using conditional probabilities at the second draw.”

Essayez ensuiteLabel the exact fractions for a 52-card deckChange the event from hearts to face cards

Ce que contient ce dessin

Comprenez les décisions qui le sous-tendent.

01First draw

Split by whether the first card is a heart.

02Second draw

Adjust the later chance because one card is gone.

03Paths

Name each two-card outcome.

Use to introduce probability trees for sampling without replacement.

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FAQ

Questions fréquentes

Why are these events dependent?

The first draw changes which cards remain for the second draw.

Can I use fractions instead?

Yes. Exact deck counts are often shown as fractions.

What does a path describe?

The ordered result of both draws.