Question

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:

• A. $\frac{3}{4}$
• B. $\frac{52}{867}$
• C. $\frac{39}{50}$
• D. $\frac{22}{425}$

Answer 1

The correct option is C $\frac{39}{50}$

$P_{\left({\overline{S}}_{\text{missig}}|\text{both found spade}\right)}=\frac{P({\overline{S}}_m\cap BFS)}{P\left(BFS\right)}=\frac{(1-\frac{13}{52})\times \frac{13}{51}\times \frac{12}{50}}{(1-\frac{13}{52})\times \frac{13}{51}\times \frac{12}{50}+\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}}=\frac{39}{50}$