Question

From a well shuffled pack of $52$ cards, few cards of same colour are missing. If $P$ (drawing a red card) $=\frac{2}{3}$ and $P$ (drawing a black card) $=\frac{1}{3}$, then which colour of cards are missing and how many?

Answer 1

Normally there are $26$ black and $26$ red cards.

So probability of drawing a red card will be $1/2$ and black card will be $1/2.$

But according to the question,

P (red) $=2/3$ and p (black) $=1/3.$

Here we can clearly understand that black cards are missing as they are less in number when compared to Red.

So red cards will be same i.e $26.$

Let $x$ be The number of cards in the new set. ( after the missing cards).

So, p $\left(red\right)=26/x.$ ----------------------- $1$

But, p $\left(red\right)=2/3.$ (Given in the question) -----$2$

From The above two equations ,

$26/x=2/3$

$x=26\times 3/2$

$x=13\times 3=39.$

So there are $39$ cards in the new set$.$

Remaining cards $=52-39=13.$

So, $13$ black cards are missing$.$