A deck of cards has red and black cards. The probability of a randomly chosen card being red is $\fr

Question

A deck of cards has red and black cards. The probability of a randomly chosen card being red is $\frac{1}{3}$. When four black card are added to the deck, the probability of choosing red becomes $\frac{1}{4}$. Then the number of cards in the deck originally is

Professor PC Thomas Classes · Answer

Solving linear proportions: $b=2r$ and $\frac{r}{3r+4} = \frac{1}{4} \Rightarrow r=4, b=8$. Original deck contains 12 cards.