Question
a deck of 108 cards contains an equal numbert of each color re yellow green and black wht is the probability that it is black
Answers
GPT-4o mini
To find the probability of drawing a black card from a deck of 108 cards that contain an equal number of yellow, green, and black cards, we first need to determine how many cards of each color are present.
Since the deck contains three colors (yellow, green, and black) and there are an equal number of each, we can divide the total number of cards (108) by the number of colors (3):
\[
\text{Number of each color} = \frac{108}{3} = 36
\]
So, there are 36 black cards in the deck.
The probability \( P \) of drawing a black card is given by the formula:
\[
P(\text{black}) = \frac{\text{Number of black cards}}{\text{Total number of cards}} = \frac{36}{108}
\]
Now, we can simplify this fraction:
\[
P(\text{black}) = \frac{36 \div 36}{108 \div 36} = \frac{1}{3}
\]
Therefore, the probability of drawing a black card from the deck is \( \frac{1}{3} \).
Since the deck contains three colors (yellow, green, and black) and there are an equal number of each, we can divide the total number of cards (108) by the number of colors (3):
\[
\text{Number of each color} = \frac{108}{3} = 36
\]
So, there are 36 black cards in the deck.
The probability \( P \) of drawing a black card is given by the formula:
\[
P(\text{black}) = \frac{\text{Number of black cards}}{\text{Total number of cards}} = \frac{36}{108}
\]
Now, we can simplify this fraction:
\[
P(\text{black}) = \frac{36 \div 36}{108 \div 36} = \frac{1}{3}
\]
Therefore, the probability of drawing a black card from the deck is \( \frac{1}{3} \).