Question

Three cards are chosen at random with replacement from a standard deck of $52$ cards. What is the probability of choosing an ace, a spade and a four?

• A. $\frac{1}{576}$
• B. $\frac{1}{676}$
• C. $\frac{5}{676}$
• D. $\frac{5}{576}$

Answer 1

The correct option is B $\frac{1}{676}$

In the deck of $52$ cards , there will be $4$ aces , $13$ spades and $4$ fours.

The probability of selecting an ace from a deck is $\frac{4}{52}=\frac{1}{13}$.

The probability of selecting a spade from a deck is $\frac{13}{52}=\frac{1}{4}$.

The probability of selecting a four from a deck is $\frac{4}{52}=\frac{1}{13}$.

The combined probability is $\frac{1}{13}\times \frac{1}{4}\times \frac{1}{13}=\frac{1}{676}$.

So the correct option is $B$.