Respuesta :
Answer:
The probability that the card drawn is a club is 0.25.
The probability that card drawn is a club, when it is given that the card is black is 0.5.
Step-by-step explanation:
In a standard deck of cards:
Total number of cards = 52
Total number of cards of each suit (club, spade,heart, diamond) = 13
The probability that the card drawn is a club is
[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25[/tex]
Therefore the probability that the card drawn is a club is 0.25.
Let A and B represents the following events:
A : Card is black
B : Card is a club
Total number of black cards = 26
[tex]P(A)=\frac{26}{52}=\frac{1}{2}=0.5[/tex]
From the above parts
[tex]P(B)=0.25[/tex]
Total number of black club cards = 13
[tex]P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25[/tex]
We need to find the probability that card drawn is a club, when it is given that the card is black.
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{0.25}{0.5}=0.5[/tex]
Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.
