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Question
A card is drawn from a well-shuffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
(i) What is the probability that both the cards are of the same suit?
(ii) What is the probability that the first card is an ace and the second card is a red queen?
Solution
\[\left( i \right) P\left( \text{ both the cards are of same suit } \right) = P\left( \text{ both the cardsare of diamond } \right) + P\left( \text{ both the cardsare of spade }\right) + P\left( \text{ both the cardsare of club } \right) + P\left( \text{ both the cards are of heart } \right)\]
\[ = \frac{13}{52} \times \frac{13}{52} + \frac{13}{52} \times \frac{13}{52} + \frac{13}{52} \times \frac{13}{52} + \frac{13}{52} \times \frac{13}{52}\]
\[ = \frac{1}{16} + \frac{1}{16} + \frac{1}{16} + \frac{1}{16}\]
\[ = \frac{4}{16}\]
\[ = \frac{1}{4}\]
\[\left( ii \right) P\left( \text{ first ace and second red queen } \right) = P\left( \text{ ace card } \right) \times P\left( \text{ red queen } \right)\]
\[ = \frac{4}{52} \times \frac{2}{52}\]
\[ = \frac{1}{338}\]
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