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 5.
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.

Explanation:

Step1: Calculate the number of favorable outcomes

In a standard deck of 52 cards, there are 4 cards with the number 5 (one 5 of hearts, one 5 of diamonds, one 5 of clubs, one 5 of spades). So the number of favorable outcomes \(n = 4\).

Step2: Calculate the probability as a fraction

The formula for probability \(P=\frac{n}{N}\), where \(n\) is the number of favorable outcomes and \(N\) is the total number of outcomes. Here \(N = 52\). So \(P=\frac{4}{52}=\frac{1}{13}\).

Step3: Calculate the probability as a decimal

To convert \(\frac{1}{13}\) to a decimal, we perform the division \(1\div13\approx0.077\).

Step4: Calculate the probability as a percent

To convert the decimal to a percent, we multiply by 100. So \(0.077\times100 = 7.7\%\).

Answer:

a) \(\frac{1}{13}\)
b) \(0.077\)
c) \(7.7\)