Question

say that a card is drawn from a standard deck of cards with no jokers. this deck has 4 suits (diamonds, spades, hearts, clubs), with 13 cards per suit (numbers 2 through 10, jack, queen, king, ace), which add up to 52 cards in total. what is the probability that the card drawn has a queen on it? submit your answer as a simplified fraction, as well as a decimal and percentage, both rounded to the hundredths place.

Explanation:

Step1: Identify favorable and total outcomes

There are 4 queens in a 52 - card deck. So the number of favorable outcomes $n(F)=4$, and the total number of outcomes $n(T) = 52$.

Step2: Calculate probability as a fraction

The probability formula is $P=\frac{n(F)}{n(T)}$. Substituting the values, we get $P=\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate probability as a decimal

To get the decimal, divide 1 by 13: $1\div13\approx0.08$.

Step4: Calculate probability as a percentage

To convert the decimal to a percentage, multiply by 100. So $0.08\times100 = 7.69\%$.

Answer:

Fraction: $\frac{1}{13}$
Decimal: $0.08$
Percent: $7.69\%$