Dice and Cards

Algebra 2 · Axiom Academy

Favorable over total is the whole idea — dice, cards, combining events, and what happens when you don't put a card back. Every probability question boils down to one ratio: favorable outcomes ÷ total outcomes . Dice and a standard 52-card deck make that ratio easy to see — and easy to test. Roll a die again and again — each face should land about 1 time in 6, in the long run. Every card is red or black — and also a rank. Pick a second condition and see how "and" and "or" combine with "red." Draw two cards in a row. If you don't put the first one back, does that change your odds on the second? Every probability is favorable ÷ total — the trick is knowing what changes the total. Compound events combine with so the overlap isn't double-counted, and whether you replace what you drew decides whether one outcome affects the next: with replacement , draws are independent; without , they aren't.

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