Question

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is \(\frac{11}{50},\) the n is equal to

Answer 1

Answer is: 2 

n cards are drawn \(\&\) are found all spade, thus remaining spades = 13 - x

remaining total cards \(=52-\mathrm{x}\)

Now given that \(\mathrm{P}(\text{ lost card is spade })=\frac{11}{50}\)

i.e. \(\frac{{ }^{13-\mathrm{n}} \mathrm{C}_{1}}{{ }^{52-\mathrm{n}} \mathrm{C}_{1}}=\frac{11}{50}\)

\(50(13-\mathrm{n})=11(52-\mathrm{n})\)

\(39 \mathrm{n}=78\)

\(\mathrm{n}=2\)