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Chapter 11: Problem 17

You draw one card from a 52-card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of drawing a king each time.

Short Answer

Expert verified
The probability of drawing a king twice in a row, with replacement and shuffling, is \( \frac{1}{169}\).

Step by step solution

01

Calculate Single Event Probability

The probability of drawing a king from a 52-card deck is calculated by dividing the number of favorable outcomes (in this case, drawing a king) by the total number of possible outcomes (drawing any card from the deck). In standard decks, there are 4 king cards and 52 total cards. Hence, the probability of drawing a king is \(\frac{4}{52} = \frac{1}{13}\).
02

Calculate Joint Probability

As per the question, the card is replaced and the deck is shuffled before drawing again. This means that the two events are independent. The probability of two independent events occurring is calculated as the product of the probabilities of each of the individual events. Thus, the probability of drawing a king twice (one after the other) is \(\frac{1}{13}\times\frac{1}{13} = \frac{1}{169}\).

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