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Chapter 2: Problem 94

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 a jack or a ten from a standard deck of playing cards is \(\frac{2}{13}\), or approximately \(0.154\) or \(15.4\%\).

Step by step solution

01

Determine the number of successful outcomes

In a standard deck of playing cards, there are 4 jacks and 4 tens, one of each in each suit. So, there are a total of 4 + 4 = 8 successful outcomes (drawing a jack or a ten).
02

Determine the total number of possible outcomes

In a standard deck of playing cards, there are 52 cards, which represent the total number of possible outcomes when drawing a single card.
03

Calculate the probability

To find the probability of drawing a jack or a ten, we divide the number of successful outcomes (8) by the total number of possible outcomes (52). This can be represented as the fraction \(\frac{8}{52}\).
04

Simplify the fraction

We can simplify the fraction \(\frac{8}{52}\) by finding the greatest common divisor (GCD) of both the numerator and the denominator. The GCD of 8 and 52 is 4. Dividing both the numerator and the denominator by 4, we get the simplified fraction: \[\frac{8}{52} = \frac{8\div4}{52\div4} = \frac{2}{13}\]
05

Express the probability as a decimal and percentage

To express the probability as a decimal, we divide the simplified numerator (2) by the simplified denominator (13): \[\frac{2}{13} = 0.153846 \approx 0.154\] Now, to express this probability as a percentage, we multiply the decimal by 100: \[0.154 \times 100 = 15.4\%\] So, the probability of drawing a jack or a ten from a standard deck of playing cards is \(\frac{2}{13}\), or approximately \(0.154\) or \(15.4\%\).

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