Question
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
Answer: Option D
Let S be the sample space
Then,
$$n(S) = $$ $${}^{52}\mathop C\nolimits_2 = $$ $$\frac{{\left( {52 \times 51} \right)}}{{\left( {2 \times 1} \right)}}$$ =1326
Let E = event of getting 2 kings out of 4
∴ $$n(E) = {}^4\mathop C\nolimits_2 = $$ $$\frac{{\left( {4 \times 3} \right)}}{{\left( {2 \times 1} \right)}}$$ = 6
∴ $$P(E) = \frac{{n(E)}}{{n(S)}} = $$ $$\frac{6}{{1326}} = \frac{1}{{221}}$$
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Let S be the sample space
Then,
$$n(S) = $$ $${}^{52}\mathop C\nolimits_2 = $$ $$\frac{{\left( {52 \times 51} \right)}}{{\left( {2 \times 1} \right)}}$$ =1326
Let E = event of getting 2 kings out of 4
∴ $$n(E) = {}^4\mathop C\nolimits_2 = $$ $$\frac{{\left( {4 \times 3} \right)}}{{\left( {2 \times 1} \right)}}$$ = 6
∴ $$P(E) = \frac{{n(E)}}{{n(S)}} = $$ $$\frac{6}{{1326}} = \frac{1}{{221}}$$
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