To determine the probability of drawing a club from a standard 52-card deck, let's break down the problem step-by-step:
1. Understand the Composition of the Deck:
A standard deck of cards contains 52 cards in total. These cards are divided into four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.
2. Identify the Favorable Outcomes:
Since we are interested in drawing a club, we focus on the number of clubs in the deck. There are 13 clubs in a standard deck.
3. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability [tex]\( P(\text{club}) \)[/tex] can be calculated as follows:
[tex]\[
P(\text{club}) = \frac{\text{Number of clubs}}{\text{Total number of cards}} = \frac{13}{52}
\][/tex]
4. Simplify the Fraction:
Simplifying the fraction:
[tex]\[
\frac{13}{52} = \frac{1}{4}
\][/tex]
5. Convert to Decimal:
The fraction [tex]\(\frac{1}{4}\)[/tex] can also be expressed as a decimal:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
Hence, the probability [tex]\( P(\text{club}) \)[/tex] of drawing a club from a standard 52-card deck is [tex]\(0.25\)[/tex].
So, we have:
[tex]\[
P(\text{club}) = 0.25
\][/tex]
