Question

Find the probability of drawing a diamond card in each of the two consecutive draws from a well-shuffled pack of cards, if the card drawn is not replaced after the first draw.

Answer 1

Let A be the event of drawing a diamond card in the first draw and B be the event of drawing a diamond card in the second draw. Then,

$P\left(A\right)=\frac{{{13}_C}_1}{{{52}_C}_1}=\frac{13}{52}=\frac{1}{4}$

After drawing a diamond card in first draw 51 cards are left out of which 12 cards are diamond cards.

And, $P\left(B|A\right)=\frac{{{12}_C}_1}{{{51}_C}_1}=\frac{12}{51}=\frac{4}{17}$

Therefore, required probability = $P\left(A\right)P\left(B|A\right)=\frac{1}{4}\times \frac{4}{17}=\frac{1}{17}$