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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

Two cards are chosen at random from a deck of 52 playig cards. What...

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?

Options

  1. A117\frac{1}{17}
  2. B317\frac{3}{17}
  3. C517\frac{5}{17}
  4. D717\frac{7}{17}

Correct answer

A. 117\frac{1}{17}

Step-by-step solution

Number of ways of selecting 2 cards from deck of  cards =52C2favourable cases =13C2\begin{aligned} & \text{ cards }={ }^{52} \mathrm{C}_2 \\ & \text{favourable cases }={ }^{13} \mathrm{C}_2\end{aligned} Probability =13C252C2=13×12252×512=13×1252×51=117=\frac{{ }^{13} C_2}{{ }^{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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