Question

You used a student deck of 52 cards and selected a card at random find (c) 2 of heart

Answer 1

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:

`\text{probability = }\frac{Number\text{ of favorable outcomes}}{Total\text{ possible outcomes of an event}}`

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:

`\begin{gathered} \text{Number of picture cards = 4 }*\text{ 3} \\ =\text{ 12} \end{gathered}`

Probability as a fraction:

`=\text{ }(12)/(52)`

In decimal:

`=\text{ }0.23`

Percent:

`\begin{gathered} =\text{ 0.23 }*\text{ 100} \\ =\text{ 23\%} \end{gathered}`

(b) 9 or 10

There are 4 cards labeled 9 and 10 each.

Probability as a fraction:

`\begin{gathered} P(9or10)=\text{ P(9) + P(10)} \\ =\text{ }(4)/(52)\text{ + }(4)/(52) \\ =\text{ }(8)/(52) \end{gathered}`

In decimal:

`=\text{ 0.15}`

In percent:

`\begin{gathered} =\text{ 0.15 }*\text{ 100} \\ =\text{ 15\%} \end{gathered}`

(c) 2 of heart

In a standard deck of cards, there are only one 2 of hearts.

Probability as a fraction:

`=\text{ }(1)/(52)`

In decimal:

`=\text{ 0.02}`

In percent:

`\begin{gathered} =\text{ 0.02 }*\text{ 100} \\ =\text{ 2\%} \end{gathered}`