If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card

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If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card

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Edana Edana 1 year 2021-09-03T16:45:37+00:00 1 Answers 18 views 0

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    2021-09-03T16:46:37+00:00

    Answer:

    0.0181 = 1.81% probability of drawing a suit first, and then a face card.

    Step-by-step explanation:

    A probability is the number of desired outcomes divided by the number of total outcomes.

    Probability of drawing a suit first:

    4 out of 52 cards are suits, so:

    [tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]

    Followed by drawing a face card:

    Considering a suit was drawn, there will be 12 faces in the 51 remaining cards. So

    [tex]P(B|A) = \frac{12}{51}[/tex]

    What is the probability of drawing a suit first, followed by drawing a face card?

    [tex]P(A \cap B) = P(A) \times P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{12}{13*51} = 0.0181[/tex]

    0.0181 = 1.81% probability of drawing a suit first, and then a face card.

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