Suppose James randomly draws a card from a standard deck of 52 cards. He then places it back into the deck and draws a second card. A standard deck of cards contains four suits: clubs, diamonds, hearts, and spades. There are 13 cards in each suit, which includes three face cards: jack, queen, and king. What is the probability that James draws a queen card as the first card and a diamond card as the second card

Question

Shelby Sparks

Mathematics

23 February, 21:14

Suppose James randomly draws a card from a standard deck of 52 cards. He then places it back into the deck and draws a second card. A standard deck of cards contains four suits: clubs, diamonds, hearts, and spades. There are 13 cards in each suit, which includes three face cards: jack, queen, and king. What is the probability that James draws a queen card as the first card and a diamond card as the second card

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Answers (1)

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Bailey Zimmerman · Answer 1

0.01923 or 1.92 %

Step-by-step explanation:

The probability of drawing a queen card out of deck is 4/52

∴ P (Q) = 4/52

there are 4 queens in a deck, one of each suit.

The probability of drawing a diamond card out of deck is 13/52

∴P (D) = 13/52

there are 13 cards in diamond suit (including the three face cards).

The total will remain 52 as he has replaced the first card and have not moved it aside

therefore, the net probability for both scenarios will be defined by calculating both probabilities.

P = P (Q) x P (D)

P = 4/52 x 13/52

P=1/52

P=0.01923 (converting into percentage)

P=0.01923 x 100%

P=1.92 %

Answer: the probability that James draws a queen card as the first card and a diamond card as the second card is 1.92%