Question

Suppose you draw two cards from a standard 52-card deck. Find the probability, when both cards are drawn without replacement, that the first card is a spade and the second card has a different suit. Give your answer as a fraction in its simplest form.

Answer 1

Given

First card to be drawn should be a spade

Second card drawn without replacement should be of different suit

Find

Probability, when both cards are drawn without replacement, that the first card is a spade and the second card has a different suit.

Explanation

Total cards = 52

Spades in a deck = 13

Probability of getting spades = 13/52

If the card drawn is not replaced then the cards will be 51

Probability of getting card from another suit = 39/51

Combined probabilty of both the

$\begin{gathered} P=\frac{13}{52}\times\frac{39}{51} \\ \\ =\frac{13}{68} \end{gathered}$

Therefore probability of the event comes out to be 13/68 in simplest form

Final Answer

Probability of the event is 13/68