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Two cards are chosen at random from a deck of 52 playig cards. What is the probability that both of them have the same value?
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The correct answer is:
$\frac{1}{17}$
Number of ways of selecting 2 cards from deck of cards $={ }^{52} \mathrm{C}_{2}$
favourable cases $={ }^{13} \mathrm{C}_{2}$
Probability $=\frac{13}{52} C_{2}=\frac{\frac{13 \times 12}{2}}{\frac{52 \times 51}{2}}=\frac{13 \times 12}{52 \times 51}=\frac{1}{17}$
favourable cases $={ }^{13} \mathrm{C}_{2}$
Probability $=\frac{13}{52} C_{2}=\frac{\frac{13 \times 12}{2}}{\frac{52 \times 51}{2}}=\frac{13 \times 12}{52 \times 51}=\frac{1}{17}$
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