Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is-
A. $$\frac{{3}}{{20}}$$
B. $$\frac{{29}}{{34}}$$
C. $$\frac{{47}}{{100}}$$
D. $$\frac{{13}}{{102}}$$
Answer: Option D
Solution(By Examveda Team)
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
$$\therefore P(E) = \frac{{n(E)}}{{n(S)}} = \frac{{169}}{{1326}} = \frac{{13}}{{102}}$$
Related Questions on Probability
A. $$\frac{{1}}{{2}}$$
B. $$\frac{{2}}{{5}}$$
C. $$\frac{{8}}{{15}}$$
D. $$\frac{{9}}{{20}}$$
A. $$\frac{{10}}{{21}}$$
B. $$\frac{{11}}{{21}}$$
C. $$\frac{{2}}{{7}}$$
D. $$\frac{{5}}{{7}}$$
A. $$\frac{{1}}{{3}}$$
B. $$\frac{{3}}{{4}}$$
C. $$\frac{{7}}{{19}}$$
D. $$\frac{{8}}{{21}}$$
E. $$\frac{{9}}{{21}}$$
What is the probability of getting a sum 9 from two throws of a dice?
A. $$\frac{{1}}{{6}}$$
B. $$\frac{{1}}{{8}}$$
C. $$\frac{{1}}{{9}}$$
D. $$\frac{{1}}{{12}}$$
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