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

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

Option: 1

\frac{25}{546}
 


Option: 2

\frac{50}{663}

 


Option: 3

\frac{25}{663}
 


Option: 4

\frac{24}{563}


Answers (1)

best_answer

Probability of both drawing the common cards \mathrm{x, P(X)=} (Probability of \mathrm{A} drawing the card \mathrm{x} and any other card \mathrm{y} ) \times (Probability of \mathrm{B} drawing the card \mathrm{x} and a curd other than \mathrm{y} )
\mathrm{ =\frac{{ }^{51} C_1}{{ }^{52} C_2} \times \frac{{ }^{50} C_1}{{ }^{60} C_2}, \forall x \text {, where } x \text { has } 52 \text { value. } }

\mathrm{\therefore Required \quad probability =\Sigma P(X) }

\mathrm{=52 \times \frac{51 \times 50 \times 4}{52 \times 51 \times 52 \times 51}=\frac{50}{663} }

Hence option 2 is correct.

 

Posted by

Ritika Jonwal

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