$$A$$ and $$B$$ draw two cards each, one after another, from a pack of well-shuffled pack of $$52$$ cards. The probability that all the four cards drawn are of the same suit is :
A.
$$\frac{{44}}{{85 \times 49}}$$
B.
$$\frac{{11}}{{85 \times 49}}$$
C.
$$\frac{{13 \times 24}}{{17 \times 25 \times 49}}$$
D.
none of these
Answer :
$$\frac{{44}}{{85 \times 49}}$$
Solution :
The probability of the four cards being spades $$ = \frac{{{}^{13}{C_2}}}{{{}^{52}{C_2}}} \times \frac{{{}^{11}{C_2}}}{{{}^{50}{C_2}}}.$$
Similarly, for other suits.
$$\therefore $$ the required probability $$ = 4 \times \frac{{{}^{13}{C_2} \times {}^{11}{C_2}}}{{{}^{52}{C_2} \times {}^{50}{C_2}}} = \frac{{44}}{{85 \times 49}}.$$
Releted MCQ Question on Statistics and Probability >> Probability
Releted Question 1
Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:
Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is
The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is
If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$ is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).
A.
$$1 - P\left( {\frac{A}{B}} \right)$$
B.
$$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C.
$$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$