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Chapter 11: Problem 16

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 jack the first time and a club the second time.

Short Answer

Expert verified
The probability of drawing a jack in the first draw and a club in the second is about 1.92% or 0.01924.

Step by step solution

01

Determine Total Outcomes and Desired Outcomes

In a standard card deck, there are 52 different cards. The probability of any event is calculated by the formula - Probability = Number of desired outcomes / Number of total outcomes. The desired outcome for drawing a jack from the deck the first time is 4 (as there are 4 jacks in a deck of 52 cards). The desired outcome for drawing a club from the deck the second time is 13 (as there are 13 clubs in a deck of 52 cards). Hence, Probability of drawing a jack = 4/52 and Probability of drawing a club = 13/52.
02

Determine Combined Probability

As these are independent events, Probability of both the events (drawing a jack and then a club) = Probability of drawing a jack * Probability of drawing a club. Substitute the probabilities into this formula to calculate.
03

Simplification

Fill in the probabilities: (4/52) * (13/52) = 52/2704 = 0.01924. Hence the probability of these events happening together is about 0.01924 or approximately 1.92%.

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