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JEE Main 20254 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 4 April · Evening Shift · Mathematics · Probability

A card from a pack of 52 cards is lost. From the remaining 51...

A card from a pack of 52 cards is lost. From the remaining 51 cards, nn cards are drawn and are found to be spades. If the probability of the lost card to be a spade is 1150\frac{11}{50}, the n is equal to

Correct answer

0

Step-by-step solution

n cards are drawn \& are found all spade, thus remaining spades =13−xremainingtotalcards=13-\mathrm{x} remaining total cards=52-x\mathrm{x}Now given that P\mathrm{P}(lostcardisspadelost card is spade)=1150\frac{11}{50} i.e. 13−nC152−nC1=115050(13−n)=11(52−n)39n=78n=2\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}$$
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