Question

From a well-shuffled deck of $52$ cards, $9$ cards are taken out one by one with replacement. Then the probability that out of $9$ cards, $5$ cards are spades, is

• A. $126\cdot \frac{81}{4^9}$
• B. $126\cdot \frac{27}{4^9}$
• C. $84\cdot \frac{81}{4^9}$
• D. $84\cdot \frac{27}{4^9}$

Answer 1

The correct option is A $126\cdot \frac{81}{4^9}$

If getting a spade is success, then probability of success is, $p=\frac{1}{4}$
So, $q=\frac{3}{4}$
$n=9$, $k=5$
So, the required probability is
${}^9{C}_5{\left(\frac{1}{4}\right)}^5\cdot {\left(\frac{3}{4}\right)}^{9-5}=126\cdot \frac{81}{4^9}$