Respuesta :
Answer:
Probability to draw a club and second card is red without replacement will be [tex]\frac{13}{102}[/tex] or 12.75%
Step-by-step explanation:
A standard deck of cards contains number of cards = 52
And a standard deck contains number of club = 13
Now the probability of first card to be a club will be
[tex]P_{1}=\frac{\text{Number of club in a deck}}{\text{Total number of cards}}[/tex]
= [tex]\frac{13}{52}=\frac{1}{4}[/tex]
Now this card is separated from the deck.
Therefore, number of remaining cards = 52 - 1 = 51
Second card has been drawn from the deck without replacement.
Since number of red cards in the deck = 13 + 13 = 26
Probability of the second card drawn = [tex]\frac{\text{Number of red cards}}{\text{Number of remaining cards}}[/tex]
[tex]P_{2}=\frac{26}{51}[/tex]
Now probability that the first card is a club and the second card is red = [tex]P_{1}\times P_{2}=\frac{1}{4}\times \frac{26}{51}[/tex]
= [tex]\frac{13}{102}[/tex]
Or [tex]\frac{13}{102}\times 100=12.75%[/tex]%
Therefore, probability to draw a club and second card is red without replacement will be [tex]\frac{13}{102}[/tex] or 12.75%
