Question

A card is lost from a pack of $52$ playing cards. From the remainder of the pack, one card is drawn and is found to be spade. The probability that the missing card is a spade is

• A. $\frac{5}{17}$
• B. $\frac{4}{17}$
• C. $\frac{3}{17}$
• D. $\frac{2}{17}$

Answer 1

Answer: (B)

Let $A$ and $B$ are the events that card lost is spade and card drawn is spade.
$P\left(\right.A\left.\right)=\frac{1}{4},P\left(\right.\bar{A}\left.\right)=\frac{3}{4}$
$P\left(\right.B/A\left.\right)=\frac{12}{51},P\left(\right.B/\bar{A}\left.\right)=\frac{13}{51}$
$P\left(\right.A/B\left.\right)=\frac{P \left(\right. A \left.\right) \cdot P \left(\right. B / A \left.\right)}{P \left(\right. A \left.\right) \cdot P \left(\right. B / A \left.\right) + P \left(\right. \bar{A} \left.\right) \cdot P \left(\right. B / A \left.\right)}$
$=\frac{\frac{1}{4} \cdot \frac{12}{51}}{\frac{1}{4} \cdot \frac{12}{51} + \frac{3}{4} \cdot \frac{13}{51}}$
$=\frac{12}{51}=\frac{4}{17}$