A card is drawn and replaced four times from a deck of 52 cards. What is the probability of getting a 4 of clubs?
A) $\frac { 1 } { 256 }$
B) $\frac { 1 } { 258 }$
C) $\frac { 1 } { 255 }$
D) $\frac { 1 } { 253 }$
E) $\frac { 1 } { 251 }$

Question

Quizplus · Accepted Answer

The probability of drawing the 4 of clubs in one draw is $\frac{1}{52}$. Since the card is replaced each time, the probability remains the same for each of the four draws. The probability of not drawing the 4 of clubs in one draw is $\frac{51}{52}$. Therefore, the probability of not drawing the 4 of clubs in four draws is $(\frac{51}{52})^4$. The probability of drawing the 4 of clubs at least once in four draws is the complement of not drawing it at all, which is $1 - (\frac{51}{52})^4$. This simplifies to approximately $\frac{1}{256}$, making option A correct.

A Card Is Drawn and Replaced Four Times from a Deck