Question

Suppose the probability experiment is to draw two cards, without replacement, from a well-shuffled, standard poker deck.What is the chance both cards will be a spade

Answer 1

Answer: The chance both cards will be a spade is  $\dfrac{1}{17}$ .

Step-by-step explanation:

We know that , in a standard deck , the total number of cards = 52

The number of spades = 13

If a person selected 2 cards,

The total number of combination of selecting 2 cards out of 52 = $^{52}C_2$

The number of combination of selecting 2 spade cards out of 13 = $^{13}C_2$

Then , the probability that both cards will be a spade=$\dfrac{^{13}C_2}{^{52}C_2}$

$\dfrac{\dfrac{13!}{2!11!}}{\dfrac{52!}{2!\times50!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]$

$=\dfrac{13\times12}{51\times52}$

$=\dfrac{1}{17}$

Hence, the chance both cards will be a spade is  $\dfrac{1}{17}$ .