Respuesta :
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:
[tex]P(Heart)=\dfrac{\text{Number of heart cards}}{\text{Total number of cards}}[/tex]
[tex]P(Heart)=\dfrac{13}{52}[/tex]
[tex]P(Heart)=\dfrac{1}{4}[/tex]
Now, the number of remaining card is 51. So, the probability of drawing a club card is:
[tex]P(club)=\dfrac{\text{Number of club cards}}{\text{Total number of remaining cards}}[/tex]
[tex]P(club)=\dfrac{13}{51}[/tex]
Using these probabilities, the probability of drawing a heart and a club in that order is:
[tex]P(\text{Heart and club})=P(\text{Heart})\times P(\text{Club})[/tex]
[tex]P(\text{Heart and club})=\dfrac{1}{4}\times \dfrac{13}{51}[/tex]
[tex]P(\text{Heart and club})=\dfrac{13}{204}[/tex]
Therefore, the required probability is [tex]\dfrac{13}{204}[/tex].
