Definition
Theoretical Probability is the ratio of the number of favorable outcomes to the total possible outcomes of an event.
Expressing probability as a formula:
[tex]\text{probability = }\frac{Number\text{ of favorable outcomes}}{Total\text{ possible outcomes of an event}}[/tex]Information about a standard deck of cards:
A standard deck of cards has four suits: hearts, clubs, spades, diamonds. Each suit has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Thus the entire deck has 52 cards total.
(a) Picture card (J, Q, and K)
In a standard deck, there are 4 Jacks, Queens, and Kings. Hence, the probability of J, Q, and K are:
[tex]\begin{gathered} \text{Number of picture cards = 4 }\times\text{ 3} \\ =\text{ 12} \end{gathered}[/tex]Probability as a fraction:
[tex]=\text{ }\frac{12}{52}[/tex]In decimal:
[tex]=\text{ }0.23[/tex]Percent:
[tex]\begin{gathered} =\text{ 0.23 }\times\text{ 100} \\ =\text{ 23\%} \end{gathered}[/tex](b) 9 or 10
There are 4 cards labeled 9 and 10 each.
Probability as a fraction:
[tex]\begin{gathered} P(9or10)=\text{ P(9) + P(10)} \\ =\text{ }\frac{4}{52}\text{ + }\frac{4}{52} \\ =\text{ }\frac{8}{52} \end{gathered}[/tex]In decimal:
[tex]=\text{ 0.15}[/tex]In percent:
[tex]\begin{gathered} =\text{ 0.15 }\times\text{ 100} \\ =\text{ 15\%} \end{gathered}[/tex](c) 2 of heart
In a standard deck of cards, there are only one 2 of hearts.
Probability as a fraction:
[tex]=\text{ }\frac{1}{52}[/tex]In decimal:
[tex]=\text{ 0.02}[/tex]In percent:
[tex]\begin{gathered} =\text{ 0.02 }\times\text{ 100} \\ =\text{ 2\%} \end{gathered}[/tex]