Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King.
A. $$\frac{{1}}{{13}}$$
B. $$\frac{{4}}{{13}}$$
C. $$\frac{{1}}{{52}}$$
D. $$\frac{{1}}{{26}}$$
Answer: Option D
Solution(By Examveda Team)
Let X be the event that cards are in a club which is not king and other is the king of club.Let Y be the event that one is any club card and other is a non-club king.
Hence, required probability:
$$\eqalign{ & = P(A) + P(B) \cr & = \frac{{^{12}{C_1}{ \times ^1}{C_1}}}{{^{52}{C_2}}} + \frac{{^{13}{C_1}{ \times ^3}{C_1}}}{{^{52}{C_2}}} \cr & = \left( {\frac{{2 \times \left( {12 \times 1} \right)}}{{52 \times 51}}} \right) + \left( {\frac{{2\left( {13 \times 3} \right)}}{{52 \times 51}}} \right) \cr & = \left( {\frac{{24 + 78}}{{52 \times 51}}} \right) \cr & = \frac{1}{{26}} \cr} $$
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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