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 not a diamond.
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 non - diamond cards

A standard deck has 52 cards. There are 13 diamond cards. So the number of non - diamond cards is \(n = 52-13=39\).

Step2: Calculate the probability as a fraction

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (non - diamond cards) is 39 and the total number of outcomes is 52. So \(P=\frac{39}{52}=\frac{3}{4}\) (by dividing numerator and denominator by 13).

Step3: Calculate the probability as a decimal

To convert \(\frac{3}{4}\) to a decimal, we perform the division \(3\div4 = 0.75\).

Step4: Calculate the probability as a percent

To convert a decimal to a percent, we multiply by 100. So \(0.75\times100 = 75.0\%\)

Answer:

a) \(\frac{3}{4}\)
b) \(0.75\)
c) \(75.0\)