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7 August, 22:11

Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one of the two cards is a face card (Jack, Queen, or King) ? (Give the answer as a decimal rounded to three decimal places.)

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  1. 7 August, 22:32
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    The probability is 0.231

    Step-by-step explanation:

    In this question, we are tasked with calculating the probability that out of two cards drawn with replacement from a pack of cards, at least one of the two is a face card.

    In a standard pack of cards, there are 52 cards.

    Now let's calculate the number of face cards we have.

    There are 12 face cards in a pack of cards. There are 4 of each of Jack, Queen or King

    The probability of drawing a face card is 12/52 = 3/13

    Now, we want to calculate the probability of at least one of the cards drawn are face cards.

    Mathematically, what we are needing to calculate is

    Probability of drawing a single face card or probability of the two being a face card

    Now let's calculate.

    The probability of the first card drawn being a face card is 3/13. The probability of the second card not being a face card will be 1-3/13 = 10/13

    The joint probability under this first set of condition will be 3/13 * 10/13 = 30/169

    Now, for the second condition, here we are considering that both cards drawn are face cards. What we have is 3/13 * 3/13 = 9/169

    Now in probabilities, whenever we are having the statement or, we add the probabilities together

    Thus, the probability here would be 30/169 + 9/169 = 39/169 = 3/13

    In decimal this will be 0.231
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