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$$\eqalign{ & n\left( S \right) = {}^{52}{C_2} = \frac{{ {52 \times 51} }}{{ {2 \times 1} }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1326 \cr} $$
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
$$\eqalign{ & {\kern 1pt} = {^{13}{C_1}{ \times ^{13}}{C_1}} \cr & {\kern 1pt} {\kern 1pt} = {13 \times 13} {\kern 1pt} {\kern 1pt} \cr & {\kern 1pt} = 169 \cr & \therefore P\left( E \right) = \frac{{n\left( E \right)}}{{n\left( S \right)}} = \frac{{169}}{{1326}} = \frac{{13}}{{102}} \cr} $$
Join The Discussion
Comments ( 1 )
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. $$\frac{{1}}{{12}}$$
Why did we choose from 13