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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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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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Mathematics
1 year
2021-09-03T16:45:37+00:00
2021-09-03T16:45:37+00:00 1 Answers
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## Answers ( )

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

Step-by-step explanation:A

probabilityis 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.