To find the probability of drawing a black card from a deck of 108 cards with an equal number of red, yellow, green, and black cards, we first need to determine how many black cards there are in the deck.
Since there are 4 colors and an equal number of each color, we can calculate the number of cards of each color by dividing the total number of cards by the number of colors:
\[ \text{Number of cards of each color} = \frac{108}{4} = 27 \]
Thus, there are 27 black cards in the deck.
The probability of drawing a black card can be calculated using the formula for probability:
\[ P(\text{black}) = \frac{\text{Number of black cards}}{\text{Total number of cards}} = \frac{27}{108} \]
Now, we can simplify this fraction:
\[ \frac{27}{108} = \frac{27 \div 27}{108 \div 27} = \frac{1}{4} \]
Therefore, the probability that a randomly chosen card is black is:
\[ \boxed{\frac{1}{4}} \]
1 answer