Interview Question: Let’s Play Cards… Again

Sample Question #139 (probability theory)

Three cards are drawn randomly from a shuffled deck of 52 play cards. What’s the probability that at least one of the cards is an Ace?

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3 Responses to Interview Question: Let’s Play Cards… Again

  1. Brett says:

    ANSWER
     
    The keyword in the question is at least. So the probability is the sum of the probabilities of drawing exactly one Ace (and there’re four Ace cards in the deck), drawing exactly two Aces, and drawing exactly three Aces. Use combinatorics to calculate the numerator and the denominator.
     

  2. Wu Chao says:

    It is easier to do another way.P=1-(no A appears in the three cards)=1-C(48,3)/C(52,3)

  3. Brett says:

    Absolutely right! superbwu brought up a really good point: every time you’re asked to find the probability of "at least" something, try the 1-P(less than that "something") approach. For instance, this approaches works well for the "what’s the probability of at least two people in my group of N people sharing the same birth month and day?" question, which is popular at quant interviews.
     

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