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Chapter 11: Problem 18

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 from a 52-card deck with replacement is \((\frac{1}{13})^2\), or approximately 0.005917159763313609.

Step by step solution

01

Determine the Probability of Drawing a King

A standard deck of cards contains 52 cards, of which 4 are kings. So the probability of drawing a king on one draw is \(\frac{4}{52}\) which simplifies to \(\frac{1}{13}\).
02

Determine the Probability of Drawing a King Twice with Replacement

Because the card is replaced after each draw, the events are independent, and the overall probability of both events occurring is the product of their individual probabilities. So the probability of drawing a king twice with replacement is \((\frac{1}{13})^2\).

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