Ques. -10

Probability Level 3

"A" draws two cards at random from a pack of $52$ cards. After returning them to the pack and shuffling it, "B" draws two cards at random. The probability that their draws contain exactly one common card is :

If you're looking to promote your Rank in JEE-MAINS-2015, then go for solving this set : Expected JEE-MAINS-2015 .

\frac{25}{546}

\frac{100}{663}

\frac{25}{663}

\frac{50}{663}

2 solutions

Vighnesh Raut
Mar 2, 2015

The probability that no card is same is

$\displaystyle{\frac { \left( \begin{matrix} 50 \\ 2 \end{matrix} \right) }{ \left( \begin{matrix} 52 \\ 2 \end{matrix} \right) } =\frac { 25\times 49 }{ 26\times 51 } }$

The probability that both cards are same is

$\displaystyle{\frac { 1 }{ \left( \begin{matrix} 52 \\ 2 \end{matrix} \right) } =\frac { 1 }{ 26\times 51 } }$

Hence, the probability that exactly one card is common is

$\displaystyle{=1-\frac { 25\times 49 }{ 26\times 51 } -\frac { 1 }{ 26\times 51 } =\frac { 50 }{ 663 }}$

Cody Martin
Feb 26, 2015

$\frac{ \left(\begin{matrix}52 \\ 1\end{matrix}\right)*\left(\begin{matrix}51 \\ 2\end{matrix}\right)*2! }{ \left(\begin{matrix}52 \\ 2\end {matrix}\right) *\left(\begin{matrix}52 \\ 2\end{matrix}\right)}=\frac{ 50 }{ 663 }$

Can you please explain your answer ?

Arpit Agarwal - 6 years, 3 months ago

sure... from first 52 cards choose a card in common in 52C1 ways now 2 cards for both of them can be anything but not same which is just 51P2 ways and total sample space can be 52C2*52C2 ( 2 cards each to be drawn from pack by both A and B) if any doubt left please tell..

Cody Martin - 6 years, 3 months ago

@Arpit Agarwal

Cody Martin - 6 years, 3 months ago

@Cody Martin – Thanks a lot Cody :) I guess I kinda overthinked for this question

Arpit Agarwal - 6 years, 3 months ago

Ques. -10

If you're looking to promote your Rank in JEE-MAINS-2015, then go for solving this set : Expected JEE-MAINS-2015 .

2 solutions

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