Question

if you randomly select a card from a well - shuffled standard deck of 52 cards, determine the probability that the card you select is a heart.
a) write your answer as a reduced fraction.
b) write your answer as a decimal, rounded to the nearest thousandth.
c) write your answer as a percent. round to the nearest tenth of a percent as needed.%
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Explanation:

Step1: Calculate the probability as a fraction

The formula for probability is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
In a standard deck of 52 cards, there are 13 hearts. So, \(P(\text{heart})=\frac{13}{52}\).
Simplifying \(\frac{13}{52}\) (divide numerator and denominator by 13), we get \(\frac{1}{4}\).

Step2: Convert the fraction to a decimal

To convert \(\frac{1}{4}\) to a decimal, we perform the division \(1\div4 = 0.25\).

Step3: Convert the decimal to a percentage

To convert a decimal to a percentage, we multiply by 100. So, \(0.25\times100 = 25.0\%\)

Answer:

a) \(\frac{1}{4}\)
b) \(0.25\)
c) \(25.0\)