Question

You decide to tell your fortune by drawing two cards from a standard deck of 52cards. What is the probability of drawing two cards of the same suite in a row? Thecards are not replaced in the deck.

Answer 1

There are 4 suits: hearts, diamonds, club, a spade. Each of them has 13 cards.

The probability of picking the first card from the deck of cards can be calculated using the formula:

$\text{Probability = }\frac{Number\text{ of required outcome}}{Total\text{ number of possible outcome}}$

Hence:

$\text{Probability = }\frac{13}{52}$

The probability of picking the second card from the same suite is:

$\text{Probability = }\frac{12}{51}$

The probability of drawing two cards of the same suite is:

$\begin{gathered} =\text{ }\frac{13}{52}\times\frac{12}{51} \\ =\text{ }\frac{156}{2652} \end{gathered}$

But there are four suites. Hence, the actual probability is:

$\begin{gathered} =\text{ }\frac{156}{2652}\text{ }\times\text{ 4} \\ =\text{ }\frac{624}{2652} \end{gathered}$

The probability of drawing two cards of the same suite in a row is 624/2652