Suppose a card is drawn at random from a standard deck. The card is then shuffled back into the deck. Then for a second time a card is drawn at random from the deck. The card is then shuffled back into the deck. Finally, for a third time a card is drawn at random from the deck. What is the probability of first drawing a red card, then a diamond, and then a face card? Do not round your intermediate computations. Round your final answer to four decimal places.

Question

Mathematics

Merle

25 March, 15:26

Suppose a card is drawn at random from a standard deck. The card is then shuffled back into the deck. Then for a second time a card is drawn at random from the deck. The card is then shuffled back into the deck. Finally, for a third time a card is drawn at random from the deck. What is the probability of first drawing a red card, then a diamond, and then a face card? Do not round your intermediate computations. Round your final answer to four decimal places.

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Answers (1)

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Jazlene Frederick · Answer 1

Probability = 0.0288

Step-by-step explanation:

For the first draw.

There are total of 52 cards in a deck of cards and a total of 26 red cards in a deck of cards.

Probability of drawing a red = 26/52

Probability = 0.5

For the second draw. Actually the initial card drawn was replaced. Total number of face cards are 12.

Probability of drawing a face card = 12/52 = 0.23076923

For the third draw.

There are 13 diamond cards in total.

Probability of a diamond = 13/52

Probability = 0.25

Probability of red, face, diamond = 0.5*0.23076923*0.25=0.028846

To four decimal place = 0.0288