A card from a pack of 52 cards is lost. From the remaining 51 cards, $n$ cards are drawn and are found to be…
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
Solution
n cards are drawn \& are found all spade, thus remaining spades $=13-\mathrm{x}$ remaining total cards $=52-\mathrm{x}$ Now given that $\mathrm{P}($ lost card is spade $)=\frac{11}{50}$ $\begin{aligned} & \text { i.e. } \frac{{ }^{13-\mathrm{n}} \mathrm{C}_1}{{ }^{52-\mathrm{n}} \mathrm{C}_1}=\frac{11}{50} \\
& 50(13-\mathrm{n})=11(52-\mathrm{n}) \\
& 39 \mathrm{n}=78 \\
& \mathrm{n}=2 \end{aligned}$