P(red card and face card)

Pre-Algebra · Axiom Academy

EXAMPLE Probability of a Red Face Card Work out the probability of drawing a card that is both red and a face card from a standard deck. One card is drawn at random from a standard 52-card deck. Find the probability that the card is both red and a face card — that is, find . Nice work. You found the probability of a compound "and" event by counting the cards that meet both conditions. "And" means intersection: for , count only the outcomes that satisfy both conditions at the same time. Don't add the two sets: the answer is the 6 overlapping cards, not 26 + 12 — adding double-counts and ignores the overlap. A Venn diagram keeps it honest: the overlap region shows exactly which cards count, so you never count a red face card twice. The same "find the intersection, then divide by the total" approach works for any "and" probability question.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.