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Chapter 35: Chapter 35

Problem 1106

Next question

If a card is drawn from a deck of playing cards, what is the probability that it will be a jack or a ten?

Short Answer

Expert verified
The probability of drawing either a jack or a ten from a standard deck of playing cards is \( \frac{2}{13} \).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Counting the jacks and tens

There are 4 suits in a deck, and each suit has 1 jack and 1 ten. So, there are 4 jacks and 4 tens in a standard deck of 52 playing cards (1 jack and 1 ten per suit). This gives us a total of 4 + 4 = 8 favorable outcomes (jacks and tens).

Step 2: Calculate the probability

To calculate the probability of drawing either a jack or a ten, we will divide the number of favorable outcomes (jacks and tens) by the total number of possible outcomes (total number of cards in the deck). This can be represented as: Probability = (Number of Jacks and Tens) / (Total Number of Cards)

Step 3: Plug in the values and solve

Now we will plug in the values we found in step 1 into the probability formula: Probability = (8) / (52)

Step 4: Simplify the fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4: Probability = \( \frac{8}{52} \) = \( \frac{2}{13} \) So, the probability of drawing either a jack or a ten from a standard deck of playing cards is \( \frac{2}{13} \).

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