Two cards are drawn randomly from a pack of 52 playing cards one after the other with replacement. If A is the event of drawing a face card in the first draw and B is the event of drawing a clubs card in the second draw, then $P\left(\frac{B}{A}\right)=$
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The keywords "with replacement" are crucial in probability problems involving sequential draws. They almost always signify that the events are independent. For independent events A and B, remember that $P(A|B) = P(A)$ and $P(B|A) = P(B)$.
Step 1: Check for Independence:
Since the cards are drawn with replacement, the outcome of the second draw is independent of the first.
Thus, \( P(B|A) = P(B) \).
Step 2: Calculate Probability of B:
Event B is drawing a clubs card.
There are 13 clubs in a deck of 52 cards.
\[ P(B) = \frac{13}{52} = \frac{1}{4} \]
Therefore, \( P(B|A) = \frac{1}{4} \).