Question

Two cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a heart and a club in that order

Answer 1

Given:

Two cards are drawn from a standard deck of cards without replacement.

To find:

The probability of drawing a heart and a club in that order.

Solution:

We have,

Total number of cards = 52

Number of cards of each suit (Spade, club, diamond, heart) = 13

The probability of drawing a heart card is:

$P(Heart)=\dfrac{\text{Number of heart cards}}{\text{Total number of cards}}$

$P(Heart)=\dfrac{13}{52}$

$P(Heart)=\dfrac{1}{4}$

Now, the number of remaining card is 51. So, the probability of drawing a club card is:

$P(club)=\dfrac{\text{Number of club cards}}{\text{Total number of remaining cards}}$

$P(club)=\dfrac{13}{51}$

Using these probabilities, the probability of drawing a heart and a club in that order is:

$P(\text{Heart and club})=P(\text{Heart})\times P(\text{Club})$

$P(\text{Heart and club})=\dfrac{1}{4}\times \dfrac{13}{51}$

$P(\text{Heart and club})=\dfrac{13}{204}$

Therefore, the required probability is $\dfrac{13}{204}$.