Question

A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is

Options

• \[\frac{44}{85 \times 49}\]

   

• \[\frac{11}{85 \times 49}\]

• \[\frac{13 \times 24}{17 \times 25 \times 49}\]

•  none of these

Answer 1

\[ \frac{44}{85 \times 49}\]
\[\text{ Total cards }  = 52\]
\[\text{ There are four suits of cards in a pack, i.e. diamond, heart, spade and club } .\]
\[P\left( \text{ all 4 cards are of same suit } \right) = P\left( \text{ all 4 cards are of diamond }  \right) + P\left( \text{ all 4 cards are of heart } \right) + P\left( \text { all 4 cards are of spade }\right) + P\left( \text{ all 4 cards are of club } \right)\]
\[ = 4 \times \frac{13}{52} \times \frac{12}{51} \times \frac{11}{50} \times \frac{10}{49}\]
\[ = 4 \times \frac{11}{85 \times 49}\]
\[ = \frac{44}{85 \times 49}\]