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If 4 cards are drawn at random from a standard deck of cards, what are the odds, or probability, that the first three will be of the same suit and the fourth of another suit?

  • Probability/Combinatorics -

    First card: any card (52/52)
    Second card: one of 12 remaining cards of the same suit (12/51)
    third card: one of 11 remaining cards of the same suit (11/50)
    fourth card: one of 39 cards of any other suit (39/49)

    Since all these are required events, use the multiplication rule to get the combined probability of all four events happening.

    Odds are P(E)/(1-P(E)) where P(E) is the probability of an event taking place.

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