Question
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is-
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 1 spade and 1 heart.
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
$$ = \left( {{}^{13}\mathop C\nolimits_1 \times {}^{13}\mathop C\nolimits_1 } \right)$$ = (13 × 13) = 169
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{169}}{{1326}} = \frac{{13}}{{102}}$$
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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 1 spade and 1 heart.
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
$$ = \left( {{}^{13}\mathop C\nolimits_1 \times {}^{13}\mathop C\nolimits_1 } \right)$$ = (13 × 13) = 169
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{169}}{{1326}} = \frac{{13}}{{102}}$$
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